Ultrastrong coupling between light and matter
Summary (5 min read)
INTRODUCTION
- Being α the natural dimensionless parameter emerging in a perturbative treatment of quantum electrodynamics, its small value allows to describe most of the quantum dynamics of the electromagnetic field by only taking into account first-order (absorption, emission) or second-order processes.
- From this crucial observation sprung a whole field of research, today called cavity quantum electrodynamics [CQED, see Fig. 1(a)], which aims to exploit different kinds of photonic resonators to modulate the coupling of light with matter.
- It took more than two decades after the observation of SC for the CQED community to begin investigating the possibility to access a regime with larger η in which higher-order processes, which would hybridize states with different number of excitations, become observable.
- As the light-matter coupling strength reaches the USC regime, it starts to become possible to modify the very nature of the light and matter degrees of freedom.
- The authors then review how USC has been reached in different experimental systems.
REGIMES AND MODELS FOR LIGHT-MATTER COUPLING
- The definitions of the WC, SC, and USC regimes compare the light-matter coupling strength g to different parameters, as shown in Fig.
- Ultrastrong coupling is not SC with larger couplings; its definition does not involve the value of losses but instead compares g to bare energies in the system.
- The ratio η which defines USC instead determines whether perturbation theory can be used, and to what extent approximations can be made in models for the light-matter interaction.
Models
- Some of the most fundamental models of light-matter interaction, the quantum Rabi, Dicke, and Hopfield models, are described in Box 1.
- In the case of the quantum Rabi model (QRM), the RWA simplifies the Hamiltonian to the standard Jaynes–Cummings model (JCM) [34] (see Table B1.I).
- In contrast to the QRM, the spectrum of the JCM is simple and well-known [35].
- These processes, often studied in quantum optics, are analogous to those described by Hint for the QRM.
- For the sake of completeness, the authors here mention three other regimes of light-matter coupling which have been investigated in the literature.
PROPERTIES OF ULTRASTRONGLY COUPLED SYSTEMS
- As η increases, several properties of coupled lightmatter systems change drastically.
- Only the quantum Rabi model (see Box 1) gives a correct picture of the energy levels for all η; various approximate methods can be used for small or large η.
- The Jaynes–Cummings model correctly predicts the Rabi splitting (dressed states) between neighboring pairs of energy levels, but fails when the system enters the USC regime.
Ground-state properties
- The difference between the USC and non-USC regimes is particularly striking for the ground state of the coupled light-matter system, as shown in Fig. 2(b)-(e).
- As η grows the coupling makes it increasingly energetically favorable to have atomic and photonic excitations in the ground state.
- As explained below, whether or not this phase transition actually occurs depends on whether an additional term, the diamagnetic term, should be included in the Hamiltonian.
- (f) Same as (a), but for the Hopfield model with (solid black curves) and without (dashed grey curves) the A2 term.
- Also in this case, the ground state contains virtual light and matter excitations.
The diamagnetic term
- In the DSC regime, the diamagnetic term can act as a potential barrier for the photonic field, localizing it away from the dipoles, leading to an effective decoupling between the light and matter degrees of freedom [63, 64].
- A similar decoupling can occur if qubit-qubit interactions are added to the Dicke model [65].
- (B2.4) The ratio of the coefficients of the diamagnetic and dipolar parts of the light-matter interaction, D/g, is thus at least as large as the normalized coupling η, with the equality in Eq. (B2.4) if a single transition saturates the sum rule.
- Those claims have attracted strong criticism [69, 70] and there is for the moment no consensus on this point.
- The historically most important role played by the dia- 8 magnetic term in CQED is linked with a series of nogo theorems [69, 73–75] seemingly demonstrating that its presence makes a system stable against superradiant phase transitions.
EXPERIMENTAL SYSTEMS WITH ULTRASTRONG COUPLING
- The first experimental demonstration of ultrastrong (η > 0.1) light-matter coupling was reported in 2009 [15].
- As shown in Fig. 3 and explained below, USC has since been achieved in several different systems and at different wavelengths of light.
Intersubband polaritons
- The USC regime was first predicted [14] and demonstrated [15] exploiting intersubband polaritons in microcavity-embedded doped quantum wells.
- In these systems, nanoscopic layers of different semiconductors create a confining potential for carriers along the growth direction, which splits electronic bands into discrete parallel subbands.
- This appealing simple model can be spoiled in more complex devices.
- Moreover, as the quantum-well width increases and multiple electron transitions become available, the intuitive picture in terms of single-particle states is lost.
- Intersubband polaritons remain a scientifically and technologically interesting system to study USC phenomenology thanks to the possibility to non-adiabatically modify the coupling strength [84], making it a promising platform for quantum vacuum-emission experiments [88, 89].
Superconducting circuits
- Superconducting circuits are a powerful platform for exploring atomic physics and quantum optics, and for QIP, since their properties (resonance frequencies, coupling strength, etc.) can be designed and even tuned in situ [7].
- This has already been widely exploited in the SC regime to, e.g., engineer quantum states and realize quantum gates.
- In cavity QED, the coupling scales as α3/2.
Organic molecules
- The USC regime has also been realized at room temperature at a variety of optical frequencies, coupling cavity photons (or, in one case, plasmons [112]) to Frenkel molecular excitons [16, 17, 113–118].
- These systems consist of thin films of organic molecules with giant dipole moments (which make it possible to reach USC) sandwiched between metal mirrors [see Fig. 3(c)] and present an interesting combination of high coupling strengths and functional capacities.
- These devices exhibit a room-temperature dispersionless angle-resolved electroluminescence with very narrow emission lines that can be exploited to realize innovative optoelectronic devices.
Optomechanics
- The concept of ultrastrong light-matter interaction can be extended to optomechanics.
- Recently, the USC limit was reached in a setup where plasmonic picocavities interacted with the vibrational degrees of freedom of individual molecules [83] [see Fig. 3(a)], achieving η = g/ωm = 0.3 (ωm is the mechanical frequency).
- The increase in coupling strength here is due to the small mode volume of the picocavity, which circumvents the diffraction limit to confine optical light in a volume measured in cubic nanometers.
- The USC limit has also been approached in circuitoptomechanical systems by using the nonlinearity of a Josephson-junction qubit to boost η [120].
VIRTUAL EXCITATIONS
- As shown above in Fig. 2, a clear difference between USC systems and those with lower coupling strength is the presence of light and matter excitations in the ground state.
- These two states contain the same number of excitations.
- Textbook quantum-optical procedures to treat open quantum systems neglect the interaction between their constituent subsystems when describing their coupling to the environment [126] (see Fig. B3).
Matter
- Reservoir Light Matter Light-Matter system Weak and strong coupling Arbitrary coupling strengths Figure B3.
- The operator X̂+ can be interpreted as the operator describing the annihilation of physical photons in the interacting system.
- The photons in the ground state of a system with an atom ultrastrongly coupled to a cavity are not only unable to leave the cavity; they are tightly bound to the atom [33].
- Another way to extract virtual photons is to use additional atomic levels.
- The virtual photons in the USC part of such a system can also be released through stimulated emission [151], which opens up interesting prospects for experimental studies of dressed states in the USC regime [137] [Fig. 4(c)].
SIMULATING ULTRASTRONG COUPLING
- The experimental effort required to achieve this regime is still considerable.
- An approach that circumvents these problems is quantum simulation [152, 153], where an easy-to-control quantum system is used to simulate the properties of the quantum model of interest.
- Several proposals for quantum simulation of USC rely on driving some part of a strongly coupled system at two frequencies.
- Then a rotating frame can be found with renormalized parameters, set by the drives, that can be in the USC regime [157–164] (drives can also be used to set effective parameters in other ways [165, 166]).
- Starting from a bare η below 10−3, a simulated η of above 0.6 was achieved and the dynamics of population revivals were observed.
ULTRASTRONG COUPLING TO A CONTINUUM
- This constitutes an interesting and, so far, less explored regime of the well-known spin-boson model [173].
- After USC to a cavity was first realized a decade ago, several theory proposals showed that superconducting circuits was a suitable platform for USC to a continuum (in this case, an open waveguide on a chip) [174–176].
- Similar to the cavity case, the ground state contains a cloud of virtual photons (in many modes) surrounding the atom [176, 178] and the atom transition frequency experiences a strong Lamb shift [171, 173, 179].
- Instead, similar to the nonlinear-optics-like processes [22] discussed later in this review, the counter-rotating terms allow various frequency-conversion processes [171, 172, 182] [Fig. 6(c)].
CONNECTIONS TO OTHER MODELS
- The quantum Rabi Hamiltonian (see Box 1) is closely related to a number of other fundamental models and emerging phenomena.
- This approach enables finding topologically protected subspaces, which may help implementing decoherence-free algorithms for QIP.
- Moreover, dark matter in cosmology may be explained through SUSY, so superconducting quantum circuits in the USC regime could in principle realize dark-matter simulations on a chip.
- The QRM is also equivalent to a Rashba-Dresselhaus model, describing, e.g., a 2DEG with spin-orbit coupling of Rashba and Dresselhaus types interacting with a perpendicular, constant magnetic field [47].
- This effect is analogous to the Higgs mechanism for the generation of masses of weak-force gauge bosons through gauge-symmetry breaking.
APPLICATIONS
- The simplest answer is that USC enables more efficient interactions.
- The coupling between a single photon and a single emitter results in significant nonlinearity, which has been used in electro-optical devices operating in the SC regime.
- Increasing η from SC to USC results in better performance of such devices, e.g., faster con- 16 trol and response even for shorter lifetime of the device components.
- Some quantum effects (including quantum gates) in specific realistic short-lifetime systems cannot be observed below USC.
Quantum information processing
- Cavity- and circuit-QED systems in the USC regime are especially useful for quantum technologies like quantum metrology (e.g., novel high-resolution spectroscopy [193] utilizing smaller linewidths and improved signal-to-noise ratio) and QIP.
- Many nonlinear-optics processes can be described in terms of higher-order perturbation theory involving virtual transitions, where the system passes from an initial state |i〉 to the final state |f〉 via a number of virtual transitions to intermediate states.
- As discussed in the preceding section, superconducting quantum circuits with USC can also be used to simulate other fundamental models and testing their predictions, e.g., in quantum field theory and solid-state physics.
- Possibilities and limitations of applying USC to change the electronic ground state of a molecular ensemble to control chemical reactions have also been investigated [19, 215].
- Some of these works [213, 214] were based on the QRM as in the standard quantum-optical approach.
CONCLUSION AND OUTLOOK
- As the authors described in this review, many intriguing physical effects have already been predicted in the USC regime of light-matter interaction.
- Related experiments have been limited to increasing the light-matter coupling strength and verifying it by standard transmission measurements.
- Now that USC has been reached in a broad range of systems, the authors believe that it is high time to explore experimentally the new interesting phenomena specific to USC and, finally, to find their useful applications.
- A few decades ago, CQED in the WC and SC regimes was following the same route, which lead to important applications in modern quantum technologies.
- The authors therefore believe that USC applications have the potential to make a profound impact.
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"Ultrastrong coupling between light ..." refers methods in this paper
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...of the quantum Rabi model (QRM), the RWA simplifies the Hamiltonian to the standard Jaynes–Cummings model (JCM) [34] (see Table B1....
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Frequently Asked Questions (15)
Q2. What is the effect of ultrastrong coupling on the physics of an atom?
Ultrastrong coupling modifies the physics of an atom in a waveguide dramatically compared to when the coupling is low enough for the RWA to be applicable.
Q3. What is the recent prediction of the coupling g?
an exponential enhancement of the coupling g was predicted with a twophoton drive (i.e., squeezing) of the cavity field [44, 45].
Q4. How can the diamagnetic term be removed from the Hamiltonian?
The diamagnetic term can in fact be removed from the Hamiltonian by performing a Bogoliubov rotation in the space of the photon operator, at the cost of a renormalization of the cavity frequency: ωc → √ ω2c + 4ωcD.
Q5. How can the intensity of the interaction between light and matter be enhanced?
While the value of α is fixed by nature, Purcell discovered in 1946 that the intensity of the interaction of an emitter with light can be enhanced or suppressed by engineering its electromagnetic environment [1].
Q6. How did Haroche and co-workers achieve a coupling strength exceeding the losses?
In 1983, Haroche and co-workers, using a collection of Rydberg atoms in a high-Q microwave cavity, managed to achieve a coupling strength exceeding the losses in the system [2].
Q7. What are some of the emerging applications of USC?
The list of emerging applications of USC goes on much longer: QIP, quantum metrology, nonlinear optics, quantum optomechanics, quantum plasmonics, superconductivity, metamaterials, quantum field theory, quantum thermodynamics, and even chemistry QED and materials science.
Q8. What is the first regime of light-matter coupling?
The first is the deepstrong-coupling [DSC, see Fig. 1(f)] regime, in which η becomes larger than one and higher-order perturbative processes are not only observable, but can become dominant.
Q9. What can be used to simulate other fundamental models?
As discussed in the preceding section, superconducting quantum circuits with USC can also be used to simulate other fundamental models and testing their predictions, e.g., in quantum field theory and solid-state physics.
Q10. What is the way to release photons from the cavity?
if the cavity is ultrastrongly coupled to an electronic two-level system, yet another way to release photons from |E0〉 is through electroluminescence [21] [Fig. 4(d)].
Q11. How can a better control of chemical reactions be achieved?
In particular, a better control of chemical reactions can be realized via polaron decoupling, induced by SC or USC, of electronic and nuclear degrees of freedom in a molecular ensemble [20].
Q12. What is the third regime of light-matter coupling?
The third is the multi-mode-strong-coupling (MMSC), where g exceeds the free spectral range of the resonator that the matter couples to.
Q13. How long did it take for the CQED community to begin investigating the possibility of accessing?
It took more than two decades after the observation of SC for the CQED community to begin investigating the possibility to access a regime with larger η in which higher-order processes, which would hybridize states with different number of excitations, become observable.
Q14. What was the first path predicted to be observed in intersubband polaritons?
In 2005, following the first path, it was predicted [14] that this regime, which was named the ultrastrongcoupling [USC, see Fig. 1(e)] regime, could be observed in intersubband polaritons thanks to the large number of electrons involved in the transitions between parallel subbands in a quantum well.
Q15. What is the second regime of light-matter coupling?
The second, the very-strong-coupling (VSC) regime, is achieved when g becomes comparable with the spacing between the excited levels of the quantum emitter.