
==== Front
Nanophotonics
Nanophotonics
nanoph
nanoph
Nanophotonics
2192-8606
2192-8614
De Gruyter

38681681
nanoph-2023-0757
10.1515/nanoph-2023-0757
Perspective
THz quantum gap: exploring potential approaches for generating and detecting non-classical states of THz light
Todorov Yanko
https://orcid.org/0000-0002-5487-9570
Dhillon Sukhdeep
https://orcid.org/0000-0002-4354-4257
Mangeney Juliette Juliette.mangeney@phys.ens.fr

Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
Corresponding author: Juliette Mangeney, Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France, E-mail: Juliette.mangeney@phys.ens.fr
29 1 2024
4 2024
13 10 16811691
30 10 2023
30 12 2023
© 2024 the author(s), published by De Gruyter, Berlin/Boston
2024
the author(s), published by De Gruyter, Berlin/Boston GmbH, Berlin/Boston
https://creativecommons.org/licenses/by/4.0/ This work is licensed under the Creative Commons Attribution 4.0 International License.
Abstract

Over the past few decades, THz technology has made considerable progress, evidenced by the performance of current THz sources and detectors, as well as the emergence of several THz applications. However, in the realm of quantum technologies, the THz spectral domain is still in its infancy, unlike neighboring spectral domains that have flourished in recent years. Notably, in the microwave domain, superconducting qubits currently serve as the core of quantum computers, while quantum cryptography protocols have been successfully demonstrated in the visible and telecommunications domains through satellite links. The THz domain has lagged behind in these impressive advancements. Today, the current gap in the THz domain clearly concerns quantum technologies. Nonetheless, the emergence of quantum technologies operating at THz frequencies will potentially have a significant impact. Indeed, THz radiation holds significant promise for wireless communications with ultimate security owing to its low sensitivity to atmospheric disturbances. Moreover, it has the potential to raise the operating temperature of solid-state qubits, effectively addressing existing scalability issues. In addition, THz radiation can manipulate the quantum states of molecules, which are recognized as new platforms for quantum computation and simulation with long range interactions. Finally, its ability to penetrate generally opaque materials or its resistance to Rayleigh scattering are very appealing features for quantum sensing. In this perspective, we will discuss potential approaches that offer exciting prospects for generating and detecting non-classical states of THz light, thereby opening doors to significant breakthroughs in THz quantum technologies.

Keywords

terahertz
quantum technology
light–matter interaction
nanostructures
QuantERAQuantERA II [G.A.n. 101017733] - QATACOMB Project Graphene FlagshipGrant JTC2023, THINQ H2020 European Research CouncilERC-COG- 820133 “LEON” ERC-COG- 863487 “UNIQUE” Agence Nationale de la RechercheQuickTera (No. ANR-22-CE09-0018) STEM2D (No. ANR-19-CE24-0015) ANR-23-GRF1-0002-01
==== Body
pmc1 Introduction

The emerging realm of quantum technologies promises unprecedented advances in fields such as sensing, high-performance computing, simulation, cryptography, and metrology. These technologies have been so far implemented predominantly in the microwave and optical regimes and have an untapped potential in the terahertz (THz) spectral range. Exploiting this frequency domain could have a number of benefits. For instance, quantum cryptography at THz frequencies is of considerable interest for wireless communications with ultimate security, as THz wireless links exhibit attenuation levels several orders of magnitude lower than free-space optical links in the presence of dust, fog, and atmospheric turbulences [1]. In addition, extending the transition frequency of most solid-state qubits (superconducting circuits or semiconductor spins) from the GHz to the THz spectral range will support efforts on increasing the operating temperature of qubits to use a simple 4He pumping system and thus overcome the scaling problems posed by limited cooling power of dilution refrigerators below 100 mK. This will also enable qubits to be manipulated at higher speeds. Furthermore, almost all polar molecules exhibit unique spectral signatures in the THz frequency range arising from transitions between rotational quantum levels [2]. As a result, THz radiation can manipulate the quantum states of many molecules, which are recognized as new platforms for quantum computation and simulation with long range interactions [3]. Finally, the ability of THz radiation to penetrate materials that are typically opaque, or its resistance to Rayleigh scattering are very valuable features for quantum applications such as quantum telecommunications and quantum sensing [4].

Non-classical states of light, such as single photons and squeezed light, are fundamental building blocks of quantum technologies with applications in quantum communication, quantum computation, quantum simulation, quantum sensing [5], [6], and quantum metrology. In this perspective, we will discuss some potential approaches that hold promise for generating and detecting non-classical states of THz light, thereby paving the way for ground breaking advancements in THz quantum technologies.

2 Generating non-classical states of THz light

In principle, any nonlinear process can produce quantum light [7], [8]. Non-linear optical processes in solid-state materials are the most widely used approach to generating quantum light. Significant progress in the generation of quantum light, including single photons, entangled photon pairs and quadrature-squeezed states, has been made over the last few decades in the fields of optics [9]–[11] and microwaves [12]–[14]. However, in the THz spectral range, the generation of squeezed light has remained elusive until now. In this section, we will present promising approaches, exploiting recent advances in nanostructures, THz components and devices, to produce THz squeezed light.

2.1 THz quantum cascade lasers (QCL)

THz QCLs are, to date, the most efficient miniaturized lasers at THz frequencies with impressive improvements in performance over the last few years, including Peltier temperature operation with milliwatt output powers [15]. Their broad gain and controlled group velocity dispersion has recently enabled compact frequency comb (FC) generation, based on four-wave mixing (FWM) processes that take place within the gain medium [16], [17]. This third order nonlinear process permits the generation of quantum correlated spectral modes where, in the simplest form, a strong central mode (ω p ) permits the generation of two correlated sidebands, the signal (ω s ) and idler (ω i ), where 2ω p = ω s + ω I (see Figure 1). As a consequence, QCLs are ideal candidates for the generation of multi-mode squeezed states of light. This permits perspectives towards THz quantum photonic platform based on chip scale quantum emitters, enabling the generation of non-classical THz radiation and/or demonstration of entanglement among different comb-emitted modes, in close analogy with squeezing effects demonstrated 25 years ago in semiconductor bipolar laser diodes [18], [19]. They can then be potentially configured as the founding blocks, in the THz spectral range, for the development of the ultimate sensitivity in spectroscopic and sensing measurements, or to increase capacity, robustness and security of selected free-space quantum communication channels.

Figure 1: Schematic representation of frequency comb formation mechanisms through degenerate and nondegenerate four-wave mixing (FWM). Ref. [20] licensed under Creative Commons Attribution 4.0 License.

2.2 A two-level system strongly coupled to a THz cavity

Alternative approaches to generating non-classical states of light are based on strong coupling between microcavity photons and quantum emitters, which in this specific case are required to be in the form of a two-level system. The strong coupling regime, achieved when the interaction between the emitter and the cavity mode surpasses the cavity loss and emitter decay, induces large optical nonlinearity at the single photon level that can be harnessed to produce non-classical light exhibiting squeezing properties [21]. As shown in Figure 2, the energy eigenstates of a two-level system strongly coupled on resonance to an optical resonator are grouped into manifolds of two-level dressed states with a non-constant energy difference between consecutive manifolds, leading to anharmonic spacing. A coherent probe beam resonant with the first-order manifold is detuned from transitions to the second manifold. Thus, once a photon is coupled to the system, it suppresses the probability of coupling a second photon of the same frequency, resulting in photon blocking. Similarly, the absorption of a first photon tuned close to the bare cavity resonance enhances the absorption of subsequent photons due to resonance with higher-order manifolds, leading to photon-induced tunneling. As a result of these two effects, the output field acquires sub-Poissonian statistics. The squeezed light stems from the quantum coherence of photon pairs emitted from the system.

Figure 2: THz two-level systems and resonators. (a) A two-level system in cavity (left). Anharmonic spacing of the levels causes phenomena such as photon blockade and photon-induced tunneling (middle). Coherent and squeezed states of light (right). (b) Images of a single graphene quantum dot transistor. Source-drain current versus gate voltage without (black curve) and with THz irradiation at frequencies from 0.27 THz to 0.38 THz (color curves) revealing satellite peaks due to THz photon-assisted tunneling process. Ref. [22] licensed under Creative Commons Attribution 4.0 License. (c) Low-temperature electrical transport through a quantum-dot nanowire single-electron transistor in the dark and illuminated states (right). Images of a planar on-chip split bow-tie antenna and of the prototypical single-electron transistor (left). Ref. [23] licensed under CC-BY-NC-ND 4.0. (d) THz photocurrent spectroscopy on H2O@C60 single molecule transistors, the excitations observed below 10 meV are identified to be the quantum rotational excitations of the water molecule. Reprinted (adapted) with permission from Ref. [24]. Copyright 2021 American Chemical Society [25]. (e) Q-factor versus the number of complementary resonating metasurfaces (right). Schematic of the THz resonator and simulation result of the focused THz beam at the interface between the front lens and the resonator field (right). Ref. [26] licensed under Creative Commons Attribution 4.0 License. (f) Representation of a Tamm cavity/LC metamaterial coupled LC resonator structure. Electric field enhancement factor in the LC metamaterial plane over a single unit cell (left). Reflection spectra of a Tamm cavity resonant at approximately 0.95 THz coupled with an LC metamaterial resonant at 0.92 THz (right), from Ref. [27]. 2023 Optica Publishing Group.

Squeezed light generation based on strong coupling of a two-level system to a cavity has previously been demonstrated in the optical range, for example in an InAs quantum dot coupled to a photonic crystal resonator [28], or in a single atom of Rb placed in a high finesse optical resonator [29]. This technique has also been also implemented in the microwave range, for example using a two-level system based on a Cooper pair box strongly coupled to a microwave coplanar resonator [30]. However, this approach remains elusive in the THz spectral range so far. In the perspective of generating squeezed light in the THz domain, the transition energy of the two-level system must be tuned in the range of few meV and the quality factor Q of the THz resonator must be high.

Two-level systems with THz resonance frequencies are mainly achieved in semiconductor quantum dots, molecules, impurity, and Rydberg atoms (see Figure 2). For instance, graphene quantum dots (QD) [31] of few tens of nanometers in diameter, defined by physical etching [22], [32], display few meV energy level spacings. These graphene QDs are very promising for THz quantum optics because they exhibit an ultrasensitive response to THz photons [33], [34] and a large THz electric dipole (d – 230 nm) [23]. Currently designed with a transition frequency in the tens of GHz, coupled double QDs obtained by electrostatic confinement in bilayer graphene open interesting perspectives as a two-level system in the THz spectral [35], as this approach prevents from localized states at the graphene edges. Gate defined QDs with a THz frequency transition have been also recently achieved using a carbon nanotube [36], a InAs/InAs0.3P0.7 quantum-dot nanowire [37] and a AlGaAs/GaAs two-dimensional electron system [25]. Alternatively, colloidal HgTe QDs of typical diameters ∼100 nm, produced by a bottom-up technique, also possess energy level spacing of few meV [24]. Several molecules are also promising as a two-level system in the THz spectral range as their vibrational and rotational modes resonate at THz frequencies. For example, individual molecule of H2 has been revealed as a two-level system with its coherent superposition exhibiting extreme sensitivity to THz electric field [38]. As well, low-energy vibrational modes of a single C60 molecule [39] and quantum rotational excitations of a water molecule have been observed in the few meV range [40]. In addition, coherent two- and three-state superpositions of the phosphorus impurity (donor) with hydrogenic states in silicon have been prepared using THz radiation [41]. At last, Rydberg atoms in a thermal vapor are characterized by strong response to electromagnetic fields with THz transitions between Rydberg levels [42], [43].

THz resonators with a high-quality factor, Q > 200, are mostly Fabry–Perot cavities [26], [27], [44], [45]. Their mode volumes are very large because they are limited by diffraction, V > (λ/2)3, which leads to very poor overlap with any sub-micrometer two-level system, such as QDs. To overcome this issue, hybrid resonators based on a Fabry–Perot cavity couple to an electronic circuit such as an LC resonator have recently been developed (see Figure 2). Indeed, LC resonators show low Q (∼10) but provide subwavelength mode volume, V < 10−5 λ 3 [46]. Hybrid resonators have recently made it possible to achieve both high Q and low V [47], [48]. The optimization of the light–matter interaction with nanoscale quantum objects is also a very relevant topic for quantum detectors of THz photons (see further).

In summary, the building blocks to achieve microcavity coupled two-level THz emitters are well present today. The next step will be to demonstrate THz squeezed radiation states from such systems, which would allow envisioning a road for performing quantum optics experiments in the THz frequency domain. However, significant effort should be provided also on the detector side, as discussed in the next section.

2.3 Ultra-strong coupling (USC) regime of THz light–matter interaction

A very intriguing way of generating non-classical light is the dynamical Casimir effect [49]. This effect consists of the generation of photons from the vacuum state in time modulated systems. It was originally described theoretically for a Fabry–Perot cavity, where one of the mirrors is semi-transparent and moving periodically: the periodic modulation of the vacuum creates radiation [50]. This case is the dynamical analogue of the famous Casimir effect, where the vacuum fluctuations create a net force on the mirrors [51]. Another vision for this effect is the Unruh radiation: this occurs from accelerated bodies because the vacuum in an accelerated frame is actually a thermal state with a finite temperature [52]. Very recently, it was theoretically demonstrated that the detection of Unruh radiation generated for very brief acceleration periods is equivalent to the electrooptic sampling of the vacuum [53], linking this physics to recent experiments in the THz spectral range [54], [55].

A first experimental demonstration of the dynamical Casimir effect was published in 2011 from a group of the University of Chalmers [51], who achieved a fast modulation of the modes of a transmission line resonator terminated by an SQUID. In 2005, Ciuti et al. [56] proposed theoretically a radically different approach, based on the electronic transitions in a semiconductor quantum well strongly coupled to a microcavity mode. Namely, Ciuti et al. examined the case where the light–matter coupling strength, Ω R , becomes a sizable fraction of the transition frequency ω 21. One thus obtains a novel regime of light–matter interaction, dubbed ultra-strong coupling (USC) regime. This regime is characterized by the breakdown of the rotating wave approximation, usually employed to solve the quantum dynamics of the system. As illustrated in Figure 3, in this regime the ground state of the coupled system, G , can no longer be written as a tensor product between the ground states of the two uncoupled systems, 0⊗F . As a result, the ground state of the USC system acquires a non-zero population of cavity photons Ga†aG∼ΩR/ω122 . Now, if the coupling constant Ω R is switched back non-adiabatically to zero, the vacuum state does have a zero-photon number 0a†a0=0 , and the excess of virtual photons present in G are released in a form of correlated pair of real photons. The intensity of this Casimir radiation depends on the rate on which Ω R is modulated [57]. The excited states of the system, the cavity polaritons, also acquire non-trivial properties and become squeezed states [51], [58], [59]. The adequate description of the emission from such states requires careful theoretical analysis [60].

Figure 3: An illustration of the dynamical Casimir effect. The ground state of the USC system is not empty but contains virtual cavity photons. An abrupt turning off of the interaction strength Ω R brings the system into an uncoupled case where the ground state of the cavity is an ordinary vacuum without photons. The virtual photons in the ground state are then radiated away in a form of correlated pair of real photons [56].

Currently, there are many implementations of the USC regime, across a vast frequency range of the electromagnetic spectrum [61]. Specifically in the THz range USC has been achieved with the electronic transitions in highly doped quantum wells [62], as well as metamaterial-coupled cyclotron resonances [63]. Yet, experimental evidence of the intriguing phenomena of dynamical Casimir effect, which initiated the story of the USC is still missing. In the THz frequency range, a very promising approach is the ultra-fast time modulation of the Rabi constant Ω R through optical pumping, which has been shown both in the case of intersubband polaritons [64], as well as Landau level polaritons [65]. The real obstacle is the detector sensitivity, as the Casimir radiation is intrinsically very week. Thus, a real effort should be provided in building very sensitive THz detectors, which is the object of the next section. However, it is clear from the above example that the THz domain provides both the devices and tools for the experimental observations of intriguing quantum electrodynamical phenomena that would be difficult to observe in other spectral domains. Another appealing approach would be to study USC in the case of few electron systems [34], [66], [67]. In that case, both the features of the USC and the intrinsic quantum fermionic non-linearities would contribute for generating non-classical states of light: still an uncharted territory both for theoreticians and experimentalists.

3 Detecting non-classical states of THz light

Because of the ultralow photon energies at THz frequencies, photodetectors in this spectral range are notoriously underdeveloped and broadband detectors of single photon or non-classical states of light are nonexistent. Only one demonstration of a single THz photon detection has been reported thus far, in a narrow band around 1.5 THz, using a quantum capacitance detector [68]. In this superconducting device, which has a noise-equivalent power of less than 10−20 WHz−1/2, the free electrons produced by photons in a superconductor penetrate a small capacitive island integrated in a resonant circuit. Besides, recent theoretical studies have predicted that superconducting magic-angle bilayer graphene device is capable of detecting single photons of ultralow energies (i.e. at THz frequencies) by utilizing its record-low heat capacity and sharp superconducting transition [69]. Here, we present alternative promising approaches to detect single THz photon with ability for photon number resolution.

Of particular interest are single photon detectors that can be realized with semiconductor nanostructures. Such realizations have been pioneered from Prof. S. Komiyama’s group from University of Tokyo [70]. The main idea of the device is to build separate absorbing region in a form of semiconductor island, separated by strong and controllable potential barriers from the rest of the device, thus resulting in a single-electron transistor. After photon absorption, the photoexcited electron is transferred in a nearby conducting channel, where it is accelerated towards a read-out circuit. The key advantage of that device is that the photon absorption changes the charging state of the insulated island, which can be read-out with a high precision [66]. Furthermore, the charge excitation has typically very long lifetime: milliseconds and even seconds [27]. Sensing a charge difference that corresponds to a single electron is then equivalent to the readout of an event that corresponds to the absorption of a single photon.

A first implementation of that idea in the THz range (∼1.7 THz) was realized with a single quantum dot under strong magnetic field [71]. The quantum dot was defined by gating 2D electron gas in GaAa/AlGaAs heterostructure. A double-dot device without magnetic field and operating at 500 GHz was also demonstrated [72]. In both cases, impressive NEPs on the order of 10−21 W/Hz0.5 were reported by the authors. In the microwave, that approach has been the subject of several theoretical studies. Modeling predicts that a double quantum dots nearby a charge detector, coupled to a high-Q microwave cavity, enable single photon detection and furthermore photon counting [73], [74] (see Figure 4). Indeed, for ideal, unity efficiency detection, the fluctuations of the charge current reproduce the statistics of the incoming photons [75].

Figure 4: Detection of non-classical states of light. (a) Working principle of a single-photon detector in the microwave range formed by two capacitively coupled GaAs/Al x Ga1−x AsGaAs/AlxGa1−x As parallel quantum dots. Reproduced with permission from Ref. [68], Copyright 2002, American Chemical Society. (b) Schematic representation and a microscope image of a charge-sensitive infrared phototransistors (up). Time trace of the photocurrent at a temperature of 14 K. The histogram of the frequency of stepwise. Reproduced with permission from Ref. [74], Copyright 2002, American Chemical Society. (c) Cartoon pictures of the process leading to a THz transport gap in a carbon nanotube quantum dot (up). SEM picture of the devices: the THz cavity is capacitively coupled to the QD in the carbon nanotube (bottom). Ref. [34] licensed under Creative Commons Attribution 4.0 License. (d) Resistance for a reference Hall bar (black lines) and for a complementary THz split-ring 140 GHz resonator embedding a Hall bar revealing a breakdown of the topological protection by cavity vacuum fields in the integer quantum Hall effect. Reproduced with permission from Ref. [76], reprinted with permission from AAAS.

Another implementation was achieved in the mid-infrared range, in the wavelength range λ = 9 µm–15 µm. In that case the detector design makes use of the same type of band-structure engineering that is used for unipolar devices [77]. The absorbing island is obtained from a thin quantum well that is connected with a conducting source-drain channel trough a triangular barrier [78]. The device, called charge sensitive infrared phototransistor (CSIP) is processed in a transistor architecture with several gates, which allow lateral insulation of the thin well as well as a reset action. Typically, the device is operated in a non-stationary regime, where the source-drain current increases slowly with time owe to the transfer of photoexcited electrons. This is the regime of photon counting. For devices where the absorbing area is small enough (∼10 µm2), the variations of the source-drain current are step-like, where each step corresponds to the detection of a photon [79]. Statistics of the size of the current steps can be related to the statistics of the photon source. In Ref. [74] this was demonstrated with a thermal source, where the authors observed a Poissonian distribution of the photon arrival events. Clearly, it is very appealing to apply the same type of detector scheme to quantum sources, where one wants to observe the quantum fluctuations of the source. Another very interesting perspective is to combine several CSIP devices in order to perform time-delayed correlation measurements of the source. However, in order to reach ultimate sensitivity of CSIPs it is imperative to reduce as much as possible its absorbing area, such as the absorption of a single photon roughly corresponds to the read-out of a single photoexcited electron [74]. To achieve this ambitious task, an interesting perspective is to employ advanced photonic architectures such as antenna-coupled metamaterials [80]–[83]. The THz range is particularly suitable for such studies, as relatively low metal loss, long wavelengths and advanced nanofabrication techniques allow exploring complex geometries for optimized subwavelength light confinement [27], [78], [84]. It should also be noted that such strategies can also lead to an improved quantum efficiency of the detectors, which has been reported to be rather low 0.1 %–1 % [67], [68], [74]. The low quantum efficiency is nevertheless not always an issue in quantum optical experiments, as the second order correlation function g2(0) is independent from it [76].

Another line of research is exploring devices operating in the ultra-strong light matter coupling regime (see Figure 4(c) and (d)). In the MIR range, this research work has been going on for at least two decades, and has been concerning mainly unipolar detector devices [85]–[87]. The latter are formidable platform for exploring the interplay between electronic transport and light–matter interaction, however still underemployed at THz frequencies. In the THz frequency range, new types of devices have been emerging [34], [35], [88], with the specific task to probe the quantum fluctuations induced by the USC regime [89]. Clearly, we arrive at a point where the THz community can strongly benefit from these developments, which are highly appealing for the realization of practical THz single-photon detectors and, more generally, the detection of non-classical states of THz light.

Furthermore, detecting the multi-mode squeezed states of light potentially generated by QCLs is a challenging task. Despite improvements over the last few years [90], detecting these quantum states requires improvements in quantum efficiency of THz detectors, such as those based around graphene transistors and improving their response through, for example, reducing the channel lengths [54], [55]. An alternative approach would be the use of coherent detection in the temporal domain using sampling techniques. This approach permits the sensitive detection of the time resolved electric field and has been applied to give the direct aspect of vacuum fluctuations in the mid-infrared [91]. Recent work has extended such concepts to show electric field correlations of THz pulses using cooled electro-optic crystals [92]. However, the response of this approach reduces at high THz frequencies (where THz QCLs operate), despite recent important investigations using on-chip electro-optic geometries. Coherent ultrafast THz photoconductive detectors can provide a potential solution here where their performances can be enhanced by engineering their THz and optical response. For example, the photoconductive material can be engineered into a resonant THz metal-insulator-metal cavity [93], permitting the coherent response to be enhanced by a factor 10 at high THz frequencies. Further, this can be combined with plasmonic interdigitated top contacts to simultaneously enhance the collection efficiency of the photoexcited carriers and the photon absorption [94]. On the actual THz QCL side, considerable efforts are being made in realising harmonic comb operation [95] to produce a spectrum of equidistant modes separated in frequency by a multiple (two to tens) of the natural Fabry–Perot mode spacing defined by the laser cavity. The advantage of a harmonic comb is that it distributes its optical power among few high-power modes, in contrast to the many weaker adjacent cavity modes of a standard dense comb. As well as facilitating the possibility of detecting quantum correlations, this enables the modes of the QCL to be easily separated (using for example, gratings) for correlation measurements.

4 Conclusion: the THz quantum gap

For many decades, the THz frequency range was referred as a technological gap in terms of the lack of viable solutions for the generation and detection of THz waves [96]. In the recent years, we have been witnessing impressive developments in terms of both emitters and detectors with commercial applications [97]. Today, the actual THz gap clearly concerns quantum technologies that have been flourishing in the neighboring spectral domains. In the microwave, superconducting qubits are currently at heart of quantum computers developed both by academia as well as high tech startups and companies. In the visible and telecom domain, quantum cryptography protocols have been demonstrated with satellite links. The THz domain, however, has been considerably lagged behind these impressive developments, despite a high potential to bring together the best of the microwave and optical regions. Based on the results shown in the current perspective, we believe that this situation could change in the next decades, as the THz domain shows a plethora of new opportunities for the development of quantum technologies. We now dispose of all building blocks not only to provide quantum technologies in line with those from the other spectral ranges, but also to open new opportunities. Indeed, the THz spectral domain holds the promise of enhanced wireless communication security, raising the operating temperature of solid-state qubits, enabling new quantum computation and simulation platforms through the manipulation of quantum states in molecules, and offering valuable perspectives for quantum sensing applications. Furthermore, the USC regime which has been already demonstrated with THz devices will permit to explore completely new quantum mechanical concepts such as ultrafast quantum gates [98], non-adiabatic electrodynamics [99] and probing fundamental quantum fluctuation [89], [92]. Also, given rapid advances being made in new quantum materials, such as 2D materials [100], and their easy coupling to Si-photonics, there is a realistic prospect of integrated devices for THz quantum optics on-chip, thus providing new platforms for developing THz quantum technologies.

Research funding: YT acknowledges financial support by the European Union’s ERC-COG- 863487 “UNIQUE”. SD acknowledges financial support by the European Union’s QuantERA II [G.A.n. 101017733] – QATACOMB Project”. JM acknowledges financial support by the European Union’s ERC Consolidator Grant LEON (Grant No. 820133), by FLAG-ERA Grant THINQ by ANR-23-GRF1-0002-01, by ANR Grant QuickTera (No. ANR-22-CE09-0018) and STEM2D (No. ANR-19-CE24-0015).

Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

Conflict of interest: Authors state no conflicts of interest.

Informed consent: Informed consent was obtained from all individuals included in this study.

Ethical approval: The conducted research is not related to either human or animals use.

Data availability: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
==== Refs
References

[1] Su K. Moeller L. Barat R. B. Federici J. F. Experimental comparison of performance degradation from terahertz and infrared wireless links in fog J. Opt. Soc. Am. A 29 2 179 2012 10.1364/josaa.29.000179
[2] Mittleman D. Jacobsen R. Neelamani R. Baraniuk R. G. Nuss M. C. Gas sensing using terahertz time-domain spectroscopy Appl. Phys. B 67 3 379 390 1998 10.1007/s003400050520
[3] Najafian K. Meir Z. Willitsch S. From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N2 Phys. Chem. Chem. Phys. 22 40 23083 2020 10.1039/d0cp03906c 33048077
[4] Kutas M. Haase B. Bickert P. Riexinger F. Molter D. von Freymann G. Terahertz quantum sensing Sci. Adv. 6 11 eaaz8065 2020 10.1126/sciadv.aaz8065 32201731
[5] Lawrie B. J. Lett P. D. Marino A. M. Pooser R. C. Quantum sensing with squeezed light ACS Photonics 6 6 1307 1318 2019 10.1021/acsphotonics.9b00250
[6] Giovannetti V. Lloyd S. Maccone L. Quantum-enhanced measurements: beating the standard quantum limit Science 306 5700 1330 1336 2004 10.1126/science.1104149 15550661
[7] Walls D. F. Squeezed states of light Nature 306 5939 141 1983 10.1038/306141a0
[8] Andersen U. L. Gehring T. Marquardt C. Leuchs G. 30 years of squeezed light generation Phys. Scr. 91 5 053001 2016 10.1088/0031-8949/91/5/053001
[9] Vahlbruch H. Mehmet M. Danzmann K. Schnabel R. Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency Phys. Rev. Lett. 117 11 110801 2016 10.1103/physrevlett.117.110801 27661673
[10] Moody G. Chang L. Steiner T. J. Bowers J. E. Chip-scale nonlinear photonics for quantum light generation AVS Quant. Sci. 2 4 041702 2020 10.1116/5.0020684
[11] Bauchrowitz J. Westphal T. Schnabel R. A graphical description of optical parametric generation of squeezed states of light Am. J. Phys. 81 10 767 771 2013 10.1119/1.4819195
[12] Castellanos-Beltran M. Irwin K. Hilton G. Vale L. R. Lehnert K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial Nat. Phys. 4 12 929 931 2008 10.1038/nphys1090
[13] Malnou M. Palken D. A. Vale L. R. Hilton G. C. Lehnert K. W. Optimal operation of a josephson parametric amplifier for vacuum squeezing Phys. Rev. Appl. 9 4 044023 2018 10.1103/physrevapplied.9.044023
[14] Li J. Wang Y.-P. You J.-Q. Zhu S.-Y. Squeezing microwaves by magnetostriction Natl. Sci. Rev. 10 5 nwac247 2023 10.1093/nsr/nwac247 37228254
[15] Khalatpour A. Paulsen A. K. Deimert C. Wasilewski Z. R. Hu Q. High-power portable terahertz laser systems Nat. Photonics 15 1 16 20 2021 10.1038/s41566-020-00707-5
[16] Burghoff D. Terahertz laser frequency combs Nat. Photonics 8 6 462 467 2014 10.1038/nphoton.2014.85
[17] Faist J. Quantum cascade laser frequency combs Nanophotonics 5 2 272 291 2016 10.1515/nanoph-2016-0015
[18] Marin F. Squeezing and intermode correlations in laser diodes Phys. Rev. Lett. 75 25 4606 1995 10.1103/physrevlett.75.4606 10059952
[19] Teich M. C. Capasso F. Saleh B. E. A. Photon-number-squeezed recombination radiation in semiconductors J. Opt. Soc. Am. B 4 10 1663 1666 1987 10.1364/josab.4.001663
[20] Vitiello M. S. Consolino L. Inguscio M. De Natale P. Toward new frontiers for terahertz quantum cascade laser frequency combs Nanophotonics 10 1 187 194 2021 10.1515/nanoph-2020-0429
[21] Shan L. Generation and modulation of non-classical light in a strongly coupled photon–emitter system Photon. Res. 10 4 989 998 2022 10.1364/prj.449106
[22] Ponomarenko L. A. Chaotic Dirac billiard in graphene quantum dots Science 320 5874 356 2008 10.1126/science.1154663 18420930
[23] Messelot S. Large terahertz electric dipole of a single graphene quantum dot Phys. Rev. Res. 4 1 L012018 2022 10.1103/physrevresearch.4.l012018
[24] Apretna T. Few picosecond dynamics of intraband transitions in THz HgTe nanocrystals Nanophotonics 10 10 2753 2763 2021 10.1515/nanoph-2021-0249
[25] Kuroyama K. Kwoen J. Arakawa Y. Hirakawa K. Coherent interaction of a-few-electron quantum dot with a terahertz optical resonator arXiv:2204.10522 2023 .
[26] Hindle F. Bocquet R. Pienkina A. Cuisset A. Mouret G. Terahertz gas phase spectroscopy using a high-finesse Fabry–Pérot cavity Optica 6 12 1449 1454 2019 10.1364/optica.6.001449
[27] Messelot S. Tamm cavity in the terahertz spectral range ACS Photonics 7 10 2906 2914 2020 10.1021/acsphotonics.0c01254
[28] Faraon A. Fushman I. Englund D. Stoltz N. Petroff P. Vučković J. Coherent generation of non-classical light on a chip via photon-induced tunnelling and blockade Nat. Phys. 4 11 859 863 2008 10.1038/nphys1078
[29] Ourjoumtsev A. Observation of squeezed light from one atom excited with two photons Nature 474 7353 623 626 2011 10.1038/nature10170 21720367
[30] Rebić S. Twamley J. Milburn G. J. Giant kerr nonlinearities in circuit quantum electrodynamics Phys. Rev. Lett. 103 15 150503 2009 10.1103/physrevlett.103.150503 19905614
[31] Trauzettel B. Bulaev D. V. Loss D. Burkard G. Spin qubits in graphene quantum dots Nat. Phys. 3 3 192 2007 10.1038/nphys544
[32] Güttinger J. Transport through graphene quantum dots Rep. Prog. Phys. 75 12 126502 2012 10.1088/0034-4885/75/12/126502 23144122
[33] Riccardi E. Ultrasensitive photoresponse of graphene quantum dots in the coulomb blockade regime to THz radiation Nano Lett. 20 7 5408 2020 10.1021/acs.nanolett.0c01800 32470310
[34] El Fatimy A. Myers-Ward R. L. Boyd A. K. Daniels K. M. Gaskill D. K. Barbara P. Epitaxial graphene quantum dots for high-performance terahertz bolometers Nat. Nanotechnol. 11 4 335 2016 10.1038/nnano.2015.303 26727199
[35] Banszerus L. Electron-hole crossover in gate-controlled bilayer graphene quantum dots Nano Lett. 20 10 7709 2020 10.1021/acs.nanolett.0c03227 32986437
[36] Valmorra F. Vacuum-field-induced THz transport gap in a carbon nanotube quantum dot Nat. Commun. 12 12 5490 2021 10.1038/s41467-021-25733-x 34531384
[37] Asgari M. Quantum-dot single-electron transistors as thermoelectric quantum detectors at terahertz frequencies Nano Lett. 21 20 8587 8594 2021 10.1021/acs.nanolett.1c02022 34618458
[38] Wang L. Xia Y. Ho W. Atomic-scale quantum sensing based on the ultrafast coherence of an H2 molecule in an STM cavity Science 376 6591 401 405 2022 10.1126/science.abn9220 35446636
[39] Du S. Yoshida K. Zhang Y. Hamada I. Hirakawa K. Terahertz dynamics of electron–vibron coupling in single molecules with tunable electrostatic potential Nat. Photonics 12 10 608 612 2018 10.1038/s41566-018-0241-1
[40] Du S. Inelastic electron transport and ortho–para fluctuation of water molecule in H2O@C60 single molecule transistors Nano Lett. 21 24 10346 10353 2021 10.1021/acs.nanolett.1c03604 34854686
[41] Chick S. Coherent superpositions of three states for phosphorous donors in silicon prepared using THz radiation Nat. Commun. 8 1 16038 2017 10.1038/ncomms16038 28737173
[42] Chen S. Terahertz electrometry via infrared spectroscopy of atomic vapor Optica 9 5 485 491 2022 10.1364/optica.456761
[43] Liu B. Electric field measurement and application based on Rydberg atoms Electromagn. Sci. 1 2 2023 0020151 10.23919/emsci.2022.0015
[44] Yee C. M. Sherwin M. S. High-Q terahertz microcavities in silicon photonic crystal slabs Appl. Phys. Lett. 94 15 154104 2009 10.1063/1.3118579
[45] Zhang Q. Collective non-perturbative coupling of 2D electrons with high-quality-factor terahertz cavity photons Nature Physics 12 11 1005 1011 2016 10.1038/nphys3850
[46] Rajabali S. An ultrastrongly coupled single terahertz meta-atom Nat. Commun. 13 1 1 2022 10.1038/s41467-022-29974-2 34983933
[47] Meng F. Thomson M. D. Klug B. Roskos H. G. Strong interaction between two photons and a plasmon of a complementary metamaterial in a terahertz dual cavity Opt. Express 29 26 42420 2021 10.1364/oe.440262
[48] Messelot S. Coeymans S. Tignon J. Dhillon S. Mangeney J. High Q and sub-wavelength THz electric field confinement in ultrastrongly coupled THz resonators Photon. Res. 11 7 1203 1216 2023 10.1364/prj.482195
[49] Dodonov V. Fifty years of the dynamical Casimir effect Physics 2 1 67 104 2020 10.3390/physics2010007
[50] Moore G. T. Quantum theory of the electromagnetic field in a variable-length one-dimensional cavity J. Math. Phys. 11 9 2679 2691 1970 10.1063/1.1665432
[51] Wilson C. M. Observation of the dynamical Casimir effect in a superconducting circuit Nature 479 7373 376 379 2011 10.1038/nature10561 22094697
[52] Unruh W. G. Notes on black-hole evaporation Phys. Rev. D 14 4 870 1976 10.1103/physrevd.14.870
[53] Onoe S. Guedes T. L. M. Moskalenko A. S. Leitenstorfer A. Burkard G. Ralph T. C. Realizing a rapidly switched Unruh–DeWitt detector through electro-optic sampling of the electromagnetic vacuum Phys. Rev. D 105 5 056023 2022 10.1103/physrevd.105.056023
[54] Viti L. Purdie D. G. Lombardo A. Ferrari A. C. Vitiello M. S. HBN-encapsulated, graphene-based, room-temperature terahertz receivers, with high speed and low noise Nano Lett. 20 5 3169 3177 2020 10.1021/acs.nanolett.9b05207 32301617
[55] Viti L. Thermoelectric graphene photodetectors with sub-nanosecond response times at terahertz frequencies Nanophotonics 10 1 89 98 2021 10.1515/nanoph-2020-0255
[56] Ciuti C. Bastard G. Carusotto I. Quantum vacuum properties of the intersubband cavity polariton field Phys. Rev. B 72 11 115303 2005 10.1103/physrevb.72.115303
[57] De Liberato S. Ciuti C. Carusotto I. Quantum vacuum radiation spectra from a semiconductor microcavity with a time-modulated vacuum Rabi frequency Phys. Rev. Lett. 98 10 103602 2007 10.1103/physrevlett.98.103602 17358533
[58] Artoni M. Birman J. L. Quantum-optical properties of polariton waves Phys. Rev. B 44 8 3736 1991 10.1103/physrevb.44.3736
[59] Artoni M. Birman J. L. Detection of optical squeezing and photon statistics in polaritons Opt. Commun. 89 2 324 334 1992 10.1016/0030-4018(92)90179-u
[60] Stassi R. Savasta S. Garziano L. Spagnolo B. Nori F. Output field-quadrature measurements and squeezing in ultrastrong cavity-QED New J. Phys. 18 12 123005 2016 10.1088/1367-2630/18/12/123005
[61] Kockum A. F. Miranowicz A. De Liberato S. Savasta S. Nori F. Ultrastrong coupling between light and matter Nat. Rev. Phys. 1 1 19 40 2019 10.1038/s42254-018-0006-2
[62] Todorov Y. Ultrastrong light-matter coupling regime with polariton dots Phys. Rev. Lett. 105 19 196402 2010 10.1103/physrevlett.105.196402 21231188
[63] Scalari G. Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial Science 335 6074 1323 1326 2012 10.1126/science.1216022 22422976
[64] Günter G. Sub-cycle switch-on of ultrastrong light–matter interaction Nature 458 7235 178 181 2009 10.1038/nature07838 19279631
[65] Mornhinweg J. Halbhuber M. Ciuti C. Bougeard D. Huber R. Lange C. Tailored subcycle nonlinearities of ultrastrong light–matter coupling Phys. Rev. Lett. 126 17 177404 2021 10.1103/physrevlett.126.177404 33988443
[66] Todorov Y. Sirtori C. Few-electron ultrastrong light-matter coupling in a quantum LC circuit Phys. Rev. X 4 4 041031 2014 10.1103/physrevx.4.041031
[67] Keller J. Few-electron ultrastrong light-matter coupling at 300 GHz with nanogap hybrid LC microcavities Nano Lett. 17 12 7410 7415 2017 10.1021/acs.nanolett.7b03228 29172537
[68] Echternach P. M. Pepper B. J. Reck T. Bradford C. M. Single photon detection of 1.5 THz radiation with the quantum capacitance detector Nat. Astron. 2 1 90 97 2018 10.1038/s41550-017-0294-y
[69] Seifert P. Magic-angle bilayer graphene nanocalorimeters: toward broadband, energy-resolving single photon detection Nano Lett. 20 5 3459 3464 2020 10.1021/acs.nanolett.0c00373 32315186
[70] Komiyama S. Astafiev O. Antonov V. Hirai H. A single-photon detector in the far-infrared range Nature 403 6768 405 407 2000 10.1038/35000166 10667787
[71] Komiyama S. Single-photon detectors in the terahertz range IEEE J. Sel. Top. Quant. Electron. 17 1 54 66 2011 10.1109/jstqe.2010.2048893
[72] Astafiev O. Komiyama S. Kutsuwa T. Antonov V. Kawaguchi Y. Hirakawa K. Single-photon detector in the microwave range Appl. Phys. Lett. 80 22 4250 4252 2002 10.1063/1.1482787
[73] Zenelaj D. Potts P. P. Samuelsson P. Full counting statistics of the photocurrent through a double quantum dot embedded in a driven microwave resonator Phys. Rev. B 106 20 205135 2022 10.1103/physrevb.106.205135
[74] Ghirri A. Cornia S. Affronte M. Microwave photon detectors based on semiconducting double quantum dots Sensors 20 14 4010 2020 10.3390/s20144010 32707648
[75] Wong C. H. Vavilov M. G. Quantum efficiency of a single microwave photon detector based on a semiconductor double quantum dot Phys. Rev. A 95 1 012325 2017 10.1103/physreva.95.012325
[76] Loudon R. The Quantum Theory of Light 2nd ed Oxford Clarendon Press 1983 274
[77] Helm M. C. The Basic Physics of Intersubband Transitions, Intersubband Transitions in Quantum Wells: Physics and Device Applications San Diego Academic Press 2000
[78] Ueda T. Komiyama S. An Z. Nagai N. Hirakawa K. Temperature dependence of the performance of charge-sensitive infrared phototransistors J. Appl. Phys. 105 6 064517 2009 10.1063/1.3087579
[79] Ueda T. An Z. Hirakawa K. Komiyama S. Charge-sensitive infrared phototransistors: characterization by an all-cryogenic spectrometer J. Appl. Phys. 103 9 093109 2008 10.1063/1.2919779
[80] Mohsen B. Auto-calibrated charge-sensitive infrared phototransistor at 9.3 µm Sensors 23 7 3635 2023 10.3390/s23073635 37050698
[81] Palaferri D. Room-temperature nine-µm-wavelength photodetectors and GHz-frequency heterodyne receivers Nature 556 7699 85 88 2018 10.1038/nature25790 29579743
[82] Jeannin M. Absorption engineering in an ultrasubwavelength quantum system Nano Lett. 20 6 4430 4436 2020 10.1021/acs.nanolett.0c01217 32407632
[83] Jeannin M. High temperature metamaterial terahertz quantum detector Appl. Phys. Lett. 117 25 251102 2020 10.1063/5.0033367
[84] Strupiechonski E. Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance Appl. Phys. Lett. 100 13 131113 2012 10.1063/1.3697660
[85] Sapienza L. Photovoltaic probe of cavity polaritons in a quantum cascade structure Appl. Phys. Lett. 90 20 201101 2007 10.1063/1.2739308
[86] Vigneron P.-B. Quantum well infrared photo-detectors operating in the strong light-matter coupling regime Appl. Phys. Lett. 114 13 131104 2019 10.1063/1.5084112
[87] Pisani F. Electronic transport driven by collective light-matter coupled states in a quantum device Nat. Commun. 14 1 3914 2023 10.1038/s41467-023-39594-z 37400430
[88] Limbacher B. Resonant tunneling diodes strongly coupled to the cavity field Appl. Phys. Lett. 116 22 221101 2020 10.1063/5.0007118
[89] Appugliese F. Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect Science 375 6584 1030 1034 2022 10.1126/science.abl5818 35239382
[90] Benea-Chelmus I.-C. Bonzon C. Maissen C. Scalari G. Beck M. Faist J. Subcycle measurement of intensity correlations in the terahertz frequency range Phys. Rev. A 93 4 043812 2016 10.1103/physreva.93.043812
[91] Riek C. Direct sampling of electric-field vacuum fluctuations Science 350 6259 420 423 2015 10.1126/science.aac9788 26429882
[92] Benea-Chelmus I. C. Settembrini F. F. Scalari G. Faist J. Electric field correlation measurements on the electromagnetic vacuum state Nature 568 7751 202 206 2019 10.1038/s41586-019-1083-9 30971847
[93] Hawecker J. Cavity-based photoconductive sources for real-time terahertz imaging Photon. Res. 8 6 858 863 2020 10.1364/prj.388219
[94] Wang N. Cakmakyapan S. Lin Y.-J. Javadi H. Jarrahiet M. Room-temperature heterodyne terahertz detection with quantum-level sensitivity Nat. Astron. 3 11 977 982 2019 10.1038/s41550-019-0828-6
[95] Wang F. Ultrafast response of harmonic modelocked THz lasers Light Sci. Appl. 9 1 51 2020 10.1038/s41377-020-0288-x 32257182
[96] Tonouchi M. Cutting-edge terahertz technology Nat. Photonics 1 2 97 105 2007 10.1038/nphoton.2007.3
[97] Dhillon S. S. The 2017 terahertz science and technology roadmap J. Phys. D: Appl. Phys. 50 4 043001 2017 10.1088/1361-6463/50/4/043001
[98] Romero G. Ballester D. Wang Y. M. Scarani V. Solano E. Ultrafast quantum gates in circuit QED Phys. Rev. Lett. 108 12 120501 2012 10.1103/physrevlett.108.120501 22540561
[99] Halbhuber M. Non-adiabatic stripping of a cavity field from electrons in the deep-strong coupling regime Nat. Photonics 14 11 675 679 2020 10.1038/s41566-020-0673-2 34221109
[100] Viti L. Vitiello M. S. Tailored nano-electronics and photonics with two-dimensional materials at terahertz frequencies J. Appl. Phys. 130 17 170903 2021 10.1063/5.0065595
