Ultrastrong Coupling Regime Research Articles

Photon blockade in a double-transmon system with ultrastrong coupling

The circuit quantum electrodynamics (QED) system has brought us into an ultrastrong and deep coupling regime in the light–matter interaction community, in which the quantum effect has attracted significant interest. In this study, we theoretically investigated the photon blockade phenomenon in a double-transmon system operating in an ultrastrong coupling regime. We considered the effect of the counter-rotating wave terms in the interaction Hamiltonian and derived the master equation in the eigenpresentation. We found that photon blockade occurred in only one of the eigenmodes, and the counter-rotating wave terms enhanced the blockade by reducing the minimum value of the second-order correlation function. This study will be beneficial for the design of single-photon devices in circuit QED systems, especially in the ultrastrong coupling regime.

Ultrastrong coupling between molecular vibrations in water and surface lattice resonances.

We investigate the vibrational ultrastrong coupling between molecular vibrations of water molecules and surface lattice resonances (SLRs) sustained by extended arrays of plasmonic microparticles. We design and fabricate an array of gold bowties, which sustain a very high field enhancement, with its SLR resonated with the OH stretching modes of water. We measure a Rabi splitting of 567 cm-1 in the strongly coupled system, whose coupling strength is 8% of the OH vibrational energy, at the onset of the ultrastrong coupling regime (10%). These results introduce metallic microparticle arrays as a platform for the investigation of ultrastrong coupling, which could be used in polaritonic chemistry to modify the dynamics of chemical reactions that require high coupling strengths.

Comparing parameterized and self-consistent approaches to abinitio cavity quantum electrodynamics for electronic strong coupling.

Molecules under strong or ultra-strong light-matter coupling present an intriguing route to modify chemical structure, properties, and reactivity. A rigorous theoretical treatment of such systems requires handling matter and photon degrees of freedom on an equal quantum mechanical footing. In the regime of molecular electronic strong or ultra-strong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of abinitio quantum chemistry, yielding an approach referred to as abinitio cavity quantum electrodynamics (ai-QED), where the photon degrees of freedom are treated at the level of cavity QED. We analyze two complementary approaches to ai-QED: (1) a parameterized ai-QED, a two-step approach where the matter degrees of freedom are computed using existing electronic structure theories, enabling the construction of rigorous ai-QED Hamiltonians in a basis of many-electron eigenstates, and (2) self-consistent ai-QED, a one-step approach where electronic structure methods are generalized to include coupling between electronic and photon degrees of freedom. Although these approaches are equivalent in their exact limits, we identify a disparity between the projection of the two-body dipole self-energy operator that appears in the parameterized approach and its exact counterpart in the self-consistent approach. We provide a theoretical argument that this disparity resolves only under the limit of a complete orbital basis and a complete many-electron basis for the projection. We present numerical results highlighting this disparity and its resolution in a particularly simple molecular system of helium hydride cation, where it is possible to approach these two complete basis limits simultaneously. In this same helium hydride system, we examine and compare the practical issue of the computational cost required to converge each approach toward the complete orbital and many-electron bases limit. Finally, we assess the aspect of photonic convergence for polar and charged species, finding comparable behavior between parameterized and self-consistent approaches.

Ultrastrong coupling limit to quantum mean force Gibbs state for anharmonic environment.

The equilibrium state of a quantum system can deviate from the Gibbs state if the system-environment (SE) coupling is not weak. An analytical expression for this mean force Gibbs state (MFGS) is known in the ultrastrong coupling (USC) regime for the Caldeira-Leggett (CL) model that assumes a harmonic environment. Here, we derive analytical expressions for the MFGS in the USC regime for more general SEmodels. For all the generalized models considered here, we find the USC state to be diagonal in the basis set by the SEinteraction, just like in the CL case. While for the generic model considered, the corresponding USC-MFGS is found to alter from the CL result, we do identify a class of models more general than the CL model for which the CL-USC result remains unchanged. We also provide numerical verification for our results. These results provide key tools for the study of strong coupling quantum thermodynamics and several quantum chemistry and biology problems under more realistic SEmodels, going beyond the CL model.

Superradiant phase transitions in ultrastrong coupling regime

Abstract One of the long-standing problems in quantum optics and laser physics is the observation of both equilibrium and non-equilibrium (Dicke) superradiant states in two-level (qubit) systems interacting with the quantized electromagnetic (EM) field. We demonstrate that the superradiant phase transition (PT) at thermal equilibrium in such a system is close to ultrastrong light–matter coupling (USC) condition, which is currently available for superconducting devices. We examine the USC regime for EM fields interacting with two-level systems located in highly connected graph nodes of photonic networks beyond the rotating wave approximation. We find that a critical matter–field coupling parameter reduces ⟨ k ⟩ times due to network peculiarities providing suitable conditions for equilibrium PT observation; ⟨ k ⟩ is a network average node degree. We study the non-equilibrium (Dicke) superradiance for the same network system and show that superradiance appears as a non-equilibrium PT to the superradiant laser operating within a bad cavity limit. We show that population inversion in this case plays the same role as the reciprocal temperature inherent to the equilibrium superradiant PT. Our results open new perspectives for experimental observation of superradiance in cavity-free systems in the gigahertz photonic regime and beyond.

Ultrastrong linear optomechanical interaction

Light-matter interaction in the ultrastrong coupling regime can be used to generate exotic ground states with two-mode squeezing and may be useful for quantum-enhanced sensing. Current demonstrations of ultrastrong coupling have been performed in fundamentally nonlinear systems. We report a cavity optomechanical system that operates in the linear coupling regime, reaching a maximum coupling of gx/Ωx=0.55±0.02. Such a system is inherently unstable, which may in the future enable strong mechanical squeezing. Published by the American Physical Society 2024

Dynamical Coulomb blockade: An all electrical probe of the ultrastrong light-matter coupling regime

The regime of ultrastrong light-matter coupling (USC) has attracted considerable interest recently, as it predicts fascinating quantum phenomena such as the presence of virtual photons in the ground state. Here we propose theoretically an approach to probe the quantum correlations in USC systems based on an electrical transport experiment. Namely, we consider the case in which the light-matter coupled system constitutes the electromagnetic environment of an ultrasmall tunnel junction operating in the regime of a dynamical Coulomb blockade (DCB). Unlike optical spectroscopy, such a probe can be seen as a nondemolition measurement of the USC system ground state. We have developed two approaches in order to evaluate the effect of the light-matter coupled states on the tunneling process. The first is a generalized, multimode Peierls substitution for the tunneling Hamiltonian. The second is based on the P(E) theory describing a DCB, where the USC system is treated as an equivalent circuit. The two approaches are consistent, whereas the second one enables us explicitly to take into account the presence of dissipation. This study has been performed for the zero-temperature case, which is pertinent for the terahertz spectral range where excitation energies are typically much higher compared to the microwave domain, where DCB was first studied. Published by the American Physical Society 2024

Dynamic Ultrastrong Coupling in a 2 nm Gap Plasmonic Cavity at the Sub-Picosecond Scale.

Localized surface plasmon resonances (LSPRs) can enhance the electromagnetic fields on metallic nanostructures upon light illumination, providing an approach for manipulating light-matter interactions at the sub-wavelength scale. However, currently, there is no thorough investigation of the physical mechanism in the dynamic formation of the strongly coupled LSPRs on sub-5 nm plasmonic cavities at the sub-picosecond scale. In this work, through femtosecond broadband transient absorption spectroscopy, we reveal the dynamic ultrastrong coupling processes in a nanoparticle-in-trench (NPiT) structure containing 2 nm gap cavities, and demonstrate a coherent motional coupling between vibrating AuNPs and the nanogaps. We achieve a maximum Rabi splitting energy of ∼660 meV in the sub-picosecond hot-electron relaxation time scale under the resonant excitation of the nanogap cavity's LSPR, reaching the ultrastrong coupling regime. This leads to a change of global vibration modes for the 2 nm gap cavity, potentially related to the dynamical Casimir effect with nanogap resonators.

Manifestation of strong and ultra-strong coupling in high-order correlation functions

Strong and ultra-strong coupling in a “cavity–single atom” system is of great interest for both fundamental and applied physics. It is considered that the increase in the coupling strength between a cavity mode and an atom leads, first, to transition from weak to strong coupling and, second, to the ultra-strong coupling regime. In this paper, we refute this common opinion and demonstrate that the transitions between the coupling regimes occur in different sequences for the correlation functions of different orders. We show that for n-th order correlation functions, the transition to the strong coupling regime requires a coupling strength approximately n2/3 times greater than the one for first order correlation functions. In contrast, the transition to the ultra-strong coupling regime manifests in the dynamics of n-th order correlation functions at less coupling strength than in the dynamics of first order correlation functions. As a result, the measurement of high-order correlation functions makes it easier to observe the ultra-strong coupling in “cavity mode–single atom.”

Tutorial on nonperturbative cavity quantum electrodynamics: is the Jaynes–Cummings model still relevant?

In this tutorial review, we briefly discuss the role that the Jaynes–Cummings model occupies in present-day research in cavity quantum electrodynamics with a particular focus on the so-called ultrastrong-coupling regime. We start by critically analyzing the various approximations required to distill such a simple model from standard quantum electrodynamics. We then discuss how many of those approximations can be, and often have been, broken in recent experiments. The consequence of these failures has been the need to abandon the Jaynes–Cummings model for more complex models. In this, the quantum Rabi model has the most prominent role, and we will rapidly survey its rich and peculiar phenomenology. We conclude the paper by showing how the Jaynes–Cummings model still plays a crucial role even in nonperturbative light–matter coupling regimes.

Spectroscopy in Nanoscopic Cavities: Models and Recent Experiments.

The ability of nanophotonic cavities to confine and store light to nanoscale dimensions has important implications for enhancing molecular, excitonic, phononic, and plasmonic optical responses. Spectroscopic signatures of processes that are ordinarily exceedingly weak such as pure absorption and Raman scattering have been brought to the single-particle limit of detection, while new emergent polaritonic states of optical matter have been realized through coupling material and photonic cavity degrees of freedom across a wide range of experimentally accessible interaction strengths. In this review, we discuss both optical and electron beam spectroscopies of cavity-coupled material systems in weak, strong, and ultrastrong coupling regimes, providing a theoretical basis for understanding the physics inherent to each while highlighting recent experimental advances and exciting future directions.

Non-Gaussian feature of the output field from a double qubit-cavity ultrastrong coupling system

We investigate the non-Gaussian feature of radiation in a circuit quantum electrodynamics (QED) system where two qubits are strongly coupled to a single-mode cavity. In the regime of ultrastrong coupling (USC), the rotating-wave approximation is not valid, and the Rabi Hamiltonian contains counter-rotating wave terms, leading to level crossing and avoided crossings in the energy spectrum. We further analyze the intensity-amplitude correlation of the output field in these two novel scenarios. In the USC regime, the creation and annihilation operators in the correlation function are replaced, allowing for the identification of non-Gaussian features in the output field. Our findings reveal that despite the absence of squeezing effects in the output light, significant non-Gaussian characteristics are present. Additionally, we demonstrate that as the driving or coupling strength increases, the non-Gaussian features of the output field become more pronounced. This suggests that USC systems hold broad potential applications in the realms of nonlinear optics and the generation of non-Gaussian states.

Electron-photon exchange-correlation approximation for quantum-electrodynamical density-functional theory

Quantum-electrodynamical density-functional theory (QEDFT) provides a promising avenue for exploring complex light-matter interactions in optical cavities for real materials. Similar to conventional density-functional theory, the Kohn-Sham formulation of QEDFT needs approximations for the generally unknown exchange-correlation functional. In addition to the usual electron-electron exchange-correlation potential, an approximation for the electron-photon exchange-correlation potential is needed. A recent electron-photon exchange functional [C. Schäfer , ], derived from the equation of motion of the nonrelativistic Pauli-Fierz Hamiltonian, shows robust performance in one-dimensional systems across weak- and strong-coupling regimes. Yet, its performance in reproducing electron densities in higher dimensions remains unexplored. Here we consider this QEDFT functional approximation from one- to three-dimensional finite systems and across weak to strong light-matter couplings. The electron-photon exchange approximation provides excellent results in the ultrastrong-coupling regime. However, to ensure accuracy also in the weak-coupling regime across higher dimensions, we introduce a computationally efficient renormalization factor for the electron-photon exchange functional, which accounts for part of the electron-photon correlation contribution. These findings extend the applicability of photon-exchange-based functionals to realistic cavity-matter systems, fostering the field of cavity QED (quantum-electrodynamics) materials engineering. Published by the American Physical Society 2024

First-order quantum phase transition in the two-qubit squeezed Rabi model

We study the ground state of the two-qubit squeezed Rabi model. Two special transformations are found to diagonalize the system Hamiltonian when each qubit’s frequency is close to the field frequency, where both the squeezing and counterrotating-wave interactions are removed, leading to an effective integrable Hamiltonian. The analytical ground state is determined and matches with numerical solutions well for a range of squeezing strengths and qubit-field detunings in the ultrastrong-coupling regime. We demonstrate that the ground state exhibits a first-order quantum phase transition at a phase boundary linearly induced by the squeezed light. We characterize the two-qubit negativity analytically and find that its two-qubit entanglement increases with the increasing squeezing strength nonlinearly. The average photon numbers of the field mode and variances of position and momentum quadratures are also analyzed and discovered to have a nonlinear relation with the squeezing strength. Finally, we discuss the experimental scheme and realization possibility of the predicted results.

Self-Hybridized Vibrational-Mie Polaritons in Water Droplets

We study the self-hybridization between Mie modes supported by water droplets with stretching and bending vibrations in water molecules. Droplets with radii >2.7 μm are found to be polaritonic on the onset of the ultrastrong light-matter coupling regime. Similarly, the effect is observed in larger deuterated water droplets at lower frequencies. Our results indicate that polaritonic states are ubiquitous and occur in water droplets in mists, fogs, and clouds. This finding may have implications not only for polaritonic physics but also for aerosol and atmospheric sciences. Published by the American Physical Society 2024

Reconciling quantum and classical spectral theories of ultrastrong coupling: role of cavity bath coupling and gauge corrections

Cavity quantum-electrodynamics (QED) is a rich area of optical physics, where extreme light–matter coupling can give rise to ultrastrong coupling. The ultrastrong coupling regime presents some fascinating uniquely quantum mechanical effects, such as ground state virtual photons and vacuum squeezing. Focusing on the widely adopted Hopfield model with cavity dissipation, we show how the linear spectrum of an ultrastrong coupled cavity and a dipole can be described either classically or quantum mechanically, but only when the quantum model includes (i) corrections to maintain gauge invariance, and (ii) a specific type of cavity bath coupling, which has so far not been identified. We also show the impact of this bath model on the quantum Rabi model, which has no classical analog in ultrastrong coupling. These results can be used to guide emerging experiments and significantly impact current models and interpretations of ultrastrong coupling between light and matter.

Boosting energy transfer between quantum devices through spectrum engineering in the dissipative ultrastrong coupling regime

The coherent energy transfer between two quantum devices (a quantum charger and a quantum battery) mediated by a photonic cavity is investigated, in presence of dissipative environments, with particular focus on the ultrastrong coupling regime. Here, very short transfer times and high charging power can be achieved in comparison with the usually addressed weak coupling case. Such phenomenology is further magnified by the presence of level crossings appearing in the energy spectrum and which reveal very robust against dissipative environmental effects. Moreover, by carefully controlling the physical parameters of the model, e.g., the matter-radiation coupling and the frequencies of the system, it is possible to tune these crossings making this device more flexible and experimentally feasible. Finally to broaden our analysis, we assume the possibility of choosing between a Fock and a coherent initial state of the cavity, with the latter showing better energetic performances. Published by the American Physical Society 2024

Extracting accurate light–matter couplings from disordered polaritons

Abstract The vacuum Rabi splitting (VRS) in molecular polaritons stands as a fundamental measure of collective light–matter coupling. Despite its significance, the impact of molecular disorder on VRS is not fully understood yet. This study delves into the complexities of VRS amidst various distributions and degrees of disorder. Our analysis provides precise analytical expressions for linear absorption, transmission, and reflection spectra, along with a “sum” rule, offering a straightforward protocol for extracting accurate collective light–matter coupling values from experimental data. Importantly, our study cautions against directly translating large VRS to the onset of ultrastrong coupling regime. Furthermore, for rectangular disorder, we witness the emergence of narrow side bands alongside a broad central peak, indicating an extended coherence lifetime even in the presence of substantial disorder. These findings not only enhance our understanding of VRS in disordered molecular systems but also open avenues for achieving prolonged coherence lifetimes between the cavity and molecules via the interplay of collective coupling and disorder.

Semiclassical Truncated-Wigner-Approximation Theory of Molecular Vibration-Polariton Dynamics in Optical Cavities.

It has been experimentally demonstrated that molecular-vibration polaritons formed by strong coupling of a molecular vibration to an infrared cavity mode can significantly modify the physical properties and chemical reactivities of various molecular systems. However, a complete theoretical understanding of the underlying mechanisms of the modifications remains elusive due to the complexity of the hybrid system, especially the collective nature of polaritonic states in systems containing many molecules. We develop here the semiclassical theory of molecular vibration-polariton dynamics based on the truncated Wigner approximation (TWA) that is tractable in large molecular systems and simultaneously captures the quantum character of photons in the optical cavity. The theory is then applied to investigate the nuclear quantum dynamics of a system of identical diatomic molecules having the ground-state Morse potential and being strongly coupled to an infrared cavity mode in the ultrastrong coupling regime. The validity of TWA is examined by comparing it with the full quantum dynamics of a single-molecule system for two different initial states in the dipole and Coulomb gauges. For the initial tensor-product ground state in the dipole gauge, which corresponds to a light-matter entangled state in the Coulomb gauge, the collective and resonance effects of molecular vibration-polariton formation on the nuclear dynamics are observed in a system of many molecules.

Harnessing quantum plexcitons for enhanced sensitivity and selectivity of creatinine sensor

Despite their widespread usage, surface plasmon resonance (SPR) sensors have several drawbacks, including limited sensitivity and the requirement for sophisticated functionalization chemistry to enhance their performance. In contrast, using quantum states for sensing may result in an enormous increase in sensor performance. These states, however, often need a rigorously controlled environment, which limits their adoption. Recently, there has been a surge of interest in employing quantum plexcitons to solve this conundrum, which has recently been proven to be resilient and robust even in ambient conditions. Here, we report the utilization of plexcitons induced through hybridization of surface plasmon and excitons in a SPR-Otto configuration for sensing creatinine molecules. Using an organic pentamer, BOBzBT2, the ultra-strong coupling regime with a Rabi splitting of 22 % of the uncoupled energy was observed and exploited to monitor the creatinine concentrations. This demonstration proposes a way to combine the benefits of an SPR-based design with the sensitivity offered by quantum plexcitons, which is beneficial for future practical quantum sensing.