Ultrastrong Coupling Regime Research Articles

Steady State in Ultrastrong Coupling Regime: Expansion and First Orders

Understanding better the dynamics and steady states of systems strongly coupled to thermal baths is a great theoretical challenge with promising applications in several fields of quantum technologies. Among several strategies to gain access to the steady state, one consists in obtaining approximate expressions of the mean force Gibbs state, the reduced state of the global system-bath thermal state, largely credited to be the steady state. Here, we present analytical expressions of corrective terms to the ultrastrong coupling limit of the mean force Gibbs state, which has been recently derived. We find that the first order term precisely coincides with the first order correction obtained from a dynamical approach—master equation in the strong-decoherence regime. This strengthens the identification of the reduced steady state with the mean force Gibbs state. Additionally, we also compare our expressions with another recent result obtained from a high temperature expansion of the mean force Gibbs state. We observe numerically a good agreement for ultra strong coupling as well as for high temperatures. This confirms the validity of all these results. In particular, we show that, in term of coherences, all three results allow one to sketch the transition from ultrastrong coupling to weak coupling.Quanta 2022; 11: 53–71.

Quantum master equations and steady states for the ultrastrong-coupling limit and the strong-decoherence limit

In the framework of the theory of open quantum systems, we derive quantum master equations for the ultrastrong system-bath coupling regime and, more generally, the strong-decoherence regime. In this regime, the strong decoherence is complemented by slow relaxation processes. We use a generalization of the F\"orster and modified Redfield perturbation theories known in the theory of excitation-energy transfer. Also, we show that the mean-force Gibbs state in the corresponding limits is stationary for the derived master equations.

Dynamical stabilization by vacuum fluctuations in a cavity: Resonant electron scattering in the ultrastrong light-matter coupling regime

We developed a theory of electron scattering by a short-range repulsive potential in a cavity. In the regime of ultrastrong electron coupling to the cavity electromagnetic field, the vacuum fluctuations of the field result in the dynamical stabilization of a quasistationary polariton state confined in the core of the repulsive potential. When the energy of a free electron coincides with the energy of the confined state, the extremely efficient resonant nonelastic scattering of the electron accompanied by emission of a cavity photon appears. This effect is discussed as a basis for possible free-electron sources of nonclassical light.

(Invited) Enhanced Water Splitting at Visible Wavelength Region Using Modal Strong Coupled Photoanode and Photocathode

Plasmon-induced hot electron transfer at the metal/semiconductor interface has attracted considerable attention as a novel mechanism to promote artificial photosynthesis under visible and near-infrared irradiation.[1-4] However, a single layer of gold nanoparticles (Au-NPs) cannot efficiently harvest light.Recently, we reported that the modal strong coupling between a Fabry–Pérot (F-P) nanocavity mode and a localized surface plasmon resonance (LSPR) facilitates water splitting reactions.[5] We used a Au-NPs/TiO2/Au-film (ATA) structure as a photoanode. The TiO2/Au-film component of this photoanode acts as F-P nanocavity. The light absorption of the ATA was promoted by the optical hybrid modes based on the strong coupling formation across a broad range of wavelengths, followed by a hot electron transfer to TiO2. We observed an 11-fold increase in the incident photon-to-current conversion efficiency (IPCE) with respect to a photoanode structure without Au-film. Importantly, the internal quantum efficiency (IQE) was enhanced 1.5 times under a strong coupling over that under uncoupled conditions.We speculated that the coupling strength of the modal strong coupling affects the hot electron transfer efficiency. To increase the coupling strength, we developed a photoanode consisting of Au-Ag alloy nanoparticles /TiO2/Au-film (AATA).[6] It was expected that the splitting energy of the modal strong coupling system increase with increasing LSPR oscillator strength by mixing Ag in the nanoparticle. The AATA structure formed under modal strong coupling with a large splitting energy of 520 meV, which can be categorized into the ultrastrong coupling regime. The AATA photoanode showed a 4.0% maximum IPCE obtained at 580 nm, and the IQE was 4.1%. Additionally, the highly efficient hot-electron injection on AATA was directly observed by transient absorption measurements. Furthermore, hybrid mode-induced water oxidation using AATA structures was performed with a Faraday efficiency of more than 70% for O2 evolution.We have applied the concept of photoanodes with modal strong coupling to photocathodes as well. As a semiconductor for constructing F-P nanocavity, we employed p-type nickel oxide (NiO) which is capable of transferring holes generated in Au-NPs and fabricated a photocathode consisting of Au-NP/NiO/Pt-film (ANP).[7] The ANP structure can absorb visible light over a wide wavelength range from 500 nm to 850 nm due to a hybrid mode based on the modal strong coupling. The IPCE based on H2evolution through water/proton reduction by hot electrons reached 0.2% at 650 nm and 0.04% at 800 nm, which was significantly larger than that of Au-NPs on NiO without Pt-film. Y. Nishijima, K. Ueno, Y. Kotake, K. Murakoshi, H. Inoue, H. Misawa, J. Phys. Chem. Lett. 2012, 3, 1248-1252. Y. Zhong, K. Ueno, Y. Mori, X. Shi, T. Oshikiri, K. Murakoshi, H. Inoue, H. Misawa, Angew. Chem. Int. Ed. 2014, 53, 10350-10354. T. Oshikiri, K. Ueno, H. Misawa, Angew. Chem. Int. Ed. 2016, 55, 3942-3946. M. Okazaki, Y. Suganami, N. Hirayama, H. Nakata, T. Oshikiri, T. Yokoi, H. Misawa, K. Maeda, ACS Appl. Energy Mater. 2020, 3, 5142–5146. X. Shi, K. Ueno, T. Oshikiri, Q. Sun, K. Sasaki, H. Misawa, Nat. Nanotechnol. 2018, 13, 953-958. Y. Suganami, T. Oshikiri, X. Shi, H. Misawa, Angew. Chem. Int. Ed. 2021, 60, 18438-18442. T. Oshikiri, H. Jo, X. Shi, and H. Misawa, Chem. Eur. J. 2022, published online, DOI: 10.1002/chem.202200288

Spin-Controlled Quantum Interference of Levitated Nanorotors.

We describe how to prepare an electrically levitated nanodiamond in a superposition of orientations via microwave driving of a single embedded nitrogen-vacancy (NV) center. Suitably aligning the magnetic field with the NV center can serve to reach the regime of ultrastrong coupling between the NV and the diamond rotation, enabling single-spin control of the particle's three-dimensional orientation. We derive the effective spin-oscillator Hamiltonian for small amplitude rotation about the equilibrium configuration and develop a protocol to create and observe quantum superpositions of the particle orientation. We discuss the impact of decoherence and argue that our proposal can be realistically implemented with near-future technology.

Micromasers as quantum batteries

We show that a micromaser is an excellent model of quantum battery. A highly excited, pure, and effectively steady state of the cavity mode, charged by coherent qubits, can be achieved, also in the ultrastrong coupling regime of field-matter interaction. Stability of these appealing features against loss of coherence of the qubits and the effect of counter-rotating terms in the interaction Hamiltonian are also discussed.

Ultrastrong Coupling of Band‐Nested Excitons in Few‐Layer Molybdenum Disulphide

AbstractThe 2D transition‐metal dichalcogenides (2D TMDCs) are an intriguing platform for studying strong light–matter interactions because they combine the electronic properties of conventional semiconductors with the optical resonances found in organic systems. However, the coupling strengths demonstrated in strong exciton–polariton coupling in the 2D TMDCs remain much lower than those found in organic systems. In this paper, a new approach is taken by utilizing the large oscillator strength of the above‐band gap C exciton in few‐layer molybdenum disulphide (FL‐MoS2). A k‐space Rabi splitting of 293 meV is shown when coupling FL‐MoS2 C excitons to surface plasmon polaritons at room temperature. This value is 11% of the uncoupled exciton energy (2.67 eV or 464 nm), ≈2× what is typically seen in the TMDCs, placing the system in the ultrastrong coupling regime. The results take a step toward finally achieving the efficient quantum coherent processes of ultrastrong coupling in a CMOS‐compatible system—the 2D TMDCs—in the visible spectrum.

Squeezed-light-induced quantum phase transition in the Jaynes-Cummings model

Quantum phase transition and quench dynamics in the Jaynes-Cummings model with squeezed light are investigated. We find a special unitary transformation that removes the nonintegrable squeezing interaction when the qubit frequency far outweighs the field frequency. The eigenenergies and the eigenstates of the normal and superradiant phases are derived analytically. We demonstrate that the system exhibits a second-order quantum phase transition at a phase-boundary-induced nonlinearly by squeezed light. This phase boundary requires neither an ultrastrong coupling regime nor multiqubits, which lessens the difficulty of the experiment. The entanglement entropy is very close to its maximum value as the squeezing strength increases in the superradiant phase. In quench dynamics, the nonlinear relation between the residual energy and the squeezing strength is obtained analytically.

Perturbative Diagonalization for Time-Dependent Strong Interactions

We present a systematic method to implement a perturbative Hamiltonian diagonalization based on the time-dependent Schrieffer-Wolff transformation. Applying our method to strong parametric interactions we show how, even in the dispersive regime, full Rabi model physics is essential to describe the dressed spectrum. Our results unveil several qualitatively different results, including realization of large energy-level shifts, tunable in magnitude and sign with the frequency and amplitude of the pump mediating the parametric interaction. Crucially, Bloch-Siegert shifts, typically thought to be important only in the ultrastrong or deep-strong coupling regimes, can be rendered large even for weak dispersive interactions to realize points of exact cancelation of dressed shifts (``blind spots'') at specific pump frequencies. The framework developed here highlights the rich physics accessible with time-dependent interactions and serves to significantly expand the functionalities for control and readout of strongly interacting quantum systems.

Quantum topology in the ultrastrong coupling regime

The coupling between two or more objects can generally be categorized as strong or weak. In cavity quantum electrodynamics for example, when the coupling strength is larger than the loss rate the coupling is termed strong, and otherwise it is dubbed weak. Ultrastrong coupling, where the interaction energy is of the same order of magnitude as the bare energies of the uncoupled objects, presents a new paradigm for quantum physics and beyond. As a consequence profound changes to well established phenomena occur, for instance the ground state in an ultrastrongly coupled system is not empty but hosts virtual excitations due to the existence of processes which do not conserve the total number of excitations. The implications of ultrastrong coupling for quantum topological systems, where the number of excitations are typically conserved, remain largely unknown despite the great utility of topological matter. Here we reveal how the delicate interplay between ultrastrong coupling and topological states manifests in a one-dimensional array. We study theoretically a dimerized chain of two-level systems within the ultrastrong coupling regime, where the combined saturation and counter-rotating terms in the Hamiltonian are shown to play pivotal roles in the rich, multi-excitation effective bandstructure. In particular, we uncover unusual topological edge states, we introduce a flavour of topological state which we call an anti-edge state, and we reveal the remarkable geometric-dependent renormalizations of the quantum vaccum. Taken together, our results provide a route map for experimentalists to characterize and explore a prototypical system in the emerging field of ultrastrong quantum topology.

In situ Tuning of the Electric-Dipole Strength of a Double-Dot Charge Qubit: Charge-Noise Protection and Ultrastrong Coupling

Semiconductor quantum dots in which electrons or holes are isolated via electrostatic potentials generated by surface gates are promising building blocks for semiconductor-based quantum technology. Here, we investigate double-quantum-dot (DQD) charge qubits in GaAs capacitively coupled to high-impedance superconducting quantum interference device array and Josephson-junction array resonators. We tune the strength of the electric-dipole interaction between the qubit and the resonator in situ using surface gates. We characterize the qubit-resonator coupling strength, the qubit decoherence, and the detuning noise affecting the charge qubit for different electrostatic DQD configurations. We find all quantities to be systematically tunable over more than one order of magnitude, resulting in reproducible decoherence rates Γ2/2π<5 MHz in the limit of high interdot capacitance. In the opposite limit, by reducing the interdot capacitance, we increase the DQD electric-dipole strength and, therefore, its coupling to the resonator. Employing a Josephson-junction array resonator with an impedance of approximately 4 kΩ and a resonance frequency of ωr/2π∼5.6 GHz, we observe a coupling strength of g/2π∼630 MHz, demonstrating the possibility to operate electrons hosted in a semiconductor DQD in the ultrastrong-coupling regime (USC). The presented results are essential for further increasing the coherence of quantum-dot-based qubits and investigating USC physics in semiconducting QDs.6 MoreReceived 26 October 2021Revised 3 April 2022Accepted 26 May 2022DOI:https://doi.org/10.1103/PhysRevX.12.031004Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information architectures & platformsQuantum information processingQuantum information with hybrid systemsQuantum information with solid state qubitsQuantum Information

Photon and phonon statistics in a qubit-plasmon-phonon ultrastrong-coupling system

We study photon/phonon statistics of a qubit-plasmon-phonon hybrid system in the ultrastrong coupling regime. The introduced qubit coupling causes parity conserving and non-conserving situations. We employ an analytic approximation approach for the parity conserving case to reveal the statistical behaviors of photons and phonons. It indicates that both photons and phonons show strong antibunching at the same frequency. Even though the bunching properties of photons/phonons occupy the dominant regions of the considered frequencies, phonons tend to weakly antibunching within the photonic strong-bunching area. In contrast, one can find that the configurations of correlation functions for both photons and phonons in the parity conserving case are squeezed towards the central frequency by parity breaking, which directly triggers the reverse statistical behaviors for the different parties at the low-frequency regions and the strong bunching properties at other frequency regions. The photon-phonon cross-correlation function also demonstrates similar parity-induced differences, indicating that the non-conserving parity induces the photon-phonon bunching behavior. We finally analyze the delayed second-order correlation function with different driving frequencies, which illustrates striking oscillations revealing the occurrence of simultaneous multiple excitations.

Regimes of cavity QED under incoherent excitation: From weak to deep strong coupling

The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.

Effective theory of lattice electrons strongly coupled to quantum electromagnetic fields

Recent experiments have revealed the tantalizing possibility of fabricating lattice electronic systems strongly coupled to quantum fluctuations of electromagnetic fields, e.g., by means of geometry confinement from a cavity or artificial gauge fields in quantum simulators. In this work, we develop a high-frequency expansion to construct the effective models for lattice electrons strongly coupled to a continuum of off-resonant photon modes with arbitrary dispersion. The theory is nonperturbative in the light-matter coupling strength, and is therefore particularly suitable for the ultrastrong light-matter coupling regime. Using the effective models, we demonstrate how the dispersion and topology of the electronic energy bands can be tuned by the cavity. In particular, quasi-one-dimensional physics can emerge in a two-dimensional square lattice due to a spatially anisotropic band renormalization, and a topologically nontrivial anomalous quantum Hall state can be induced in a honeycomb lattice when the cavity setup breaks time-reversal symmetry. We also demonstrate that the photon-mediated interaction induces an unconventional superconducting paired phase distinct from the pair-density-wave state discussed in models with truncated light-matter coupling. Finally, we study a realistic setup of a Fabry-P\'{e}rot cavity. Our work provides a systematic framework to explore the emergent phenomena due to strong light-matter coupling and points out new directions of engineering orders and topological states in solids.

Organic charged polaritons in the ultrastrong coupling regime

We embedded an all-hydrocarbon-based carbocation in a metallic microcavity that was tuned to resonance with an electronic transition of the carbocation. The measured Rabi splitting was 41% of the excitation energy, putting the system well into the ultrastrong coupling regime. Importantly, due to the intrinsic charge on the carbocation, the polaritons that form carry a significant charge fraction $0.55 e_0$ and a large charge-to-mass ratio ($\sim 2400 e_0 / m_0$). Moreover, the ground state of the ultrastrongly coupled system is calculated to carry about one percent of one elementary charge, implying a potentially enhanced charge transport across the molecules. These unique properties of our system, together with its convenient preparation, provide a practical platform to study charged polaritons in the ultrastrong coupling regime.

Mechanical Squeezing via Unstable Dynamics in a Microcavity.

We theoretically show that strong mechanical quantum squeezing in a linear optomechanical system can be rapidly generated through the dynamical instability reached in the far red-detuned and ultrastrong coupling regime. We show that this mechanism, which harnesses unstable multimode quantum dynamics, is particularly suited to levitated optomechanics, and we argue for its feasibility for the case of a levitated nanoparticle coupled to a microcavity via coherent scattering. We predict that for submillimeter-sized cavities the particle motion, initially thermal and well above its ground state, becomes mechanically squeezed by tens of decibels on a microsecond timescale. Our results bring forth optical microcavities in the unresolved sideband regime as powerful mechanical squeezers for levitated nanoparticles, and hence as key tools for quantum-enhanced inertial and force sensing.

Cavity engineering of Hubbard U via phonon polaritons

Pump-probe experiments have suggested the possibility to control electronic correlations by driving infrared-active (IR-active) phonons with resonant midinfrared laser pulses. In this work we study two possible microscopic nonlinear electron-phonon interactions behind these observations, namely coupling of the squared lattice displacement either to the electronic density or to the double occupancy. We investigate whether photon-phonon coupling to quantized light in an optical cavity enables similar control over electronic correlations. We first show that inside a dark cavity electronic interactions increase, ruling out the possibility that T c in superconductors can be enhanced via effectively decreased electron-electron repulsion through nonlinear electron-phonon coupling in a cavity. We further find that upon driving the cavity, electronic interactions decrease. Two different regimes emerge: (i) a strong coupling regime where the phonons show a delayed response at a time proportional to the inverse coupling strength, and (ii) an ultra-strong coupling regime where the response is immediate when driving the phonon polaritons resonantly. We further identify a distinctive feature in the electronic spectral function when electrons couple to phonon polaritons involving an IR-active phonon mode, namely the splitting of the shake-off band into three bands. This could potentially be observed by angle-resolved photoemission spectroscopy.

Gauge-independent emission spectra and quantum correlations in the ultrastrong coupling regime of open system cavity-QED

Abstract A quantum dipole interacting with an optical cavity is one of the key models in cavity quantum electrodynamics (cavity-QED). To treat this system theoretically, the typical approach is to truncate the dipole to two levels. However, it has been shown that in the ultrastrong-coupling regime, this truncation naively destroys gauge invariance. By truncating in a manner consistent with the gauge principle, we introduce master equations for open systems to compute gauge-invariant emission spectra, photon flux rates, and quantum correlation functions which show significant disagreement with previous results obtained using the standard quantum Rabi model. Explicit examples are shown using both the dipole gauge and the Coulomb gauge.

Direct Visualization of Ultrastrong Coupling between Luttinger-Liquid Plasmons and Phonon Polaritons.

Ultrastrong coupling of light and matter creates new opportunities to modify chemical reactions or develop novel nanoscale devices. One-dimensional Luttinger-liquid plasmons in metallic carbon nanotubes are long-lived excitations with extreme electromagnetic field confinement. They are promising candidates to realize strong or even ultrastrong coupling at infrared frequencies. We applied near-field polariton interferometry to examine the interaction between propagating Luttinger-liquid plasmons in individual carbon nanotubes and surface phonon polaritons of silica and hexagonal boron nitride. We extracted the dispersion relation of the hybrid Luttinger-liquid plasmon–phonon polaritons (LPPhPs) and explained the observed phenomena by the coupled harmonic oscillator model. The dispersion shows pronounced mode splitting, and the obtained value for the normalized coupling strength shows we reached the ultrastrong coupling regime with both native silica and hBN phonons. Our findings predict future applications to exploit the extraordinary properties of carbon nanotube plasmons, ranging from nanoscale plasmonic circuits to ultrasensitive molecular sensing.

Extended Dicke quantum battery with interatomic interactions and driving field

We investigate the charging process of quantum battery (QB) systems in an extended Dicke model with both atomic interactions and an external driving field. We focus on the effects of the atomic interaction and the external driving field on the charging performance of the QB and find that the maximum stored energy of the QB has a critical phenomenon. We analyze the critical behavior and obtain the analytical expression of the critical atomic interaction. The dependence of the maximum stored energy, the energy quantum fluctuations, and the maximum charging power on the number $N$ of the two-level systems are also discussed. In particular, for the maximum charging power, we obtain the quantum advantage of the QB, which approximately satisfies a superlinear scaling relation ${P}_{\text{max}}\ensuremath{\propto}{N}^{\ensuremath{\alpha}}$, where scaling exponent $\ensuremath{\alpha}$ varies with the number $N$ of the two-level systems. In the ultrastrong coupling regime, the atomic interaction can lead to faster battery charging, and the quantum advantage $\ensuremath{\alpha}=1.88$ can be achieved. While in the deep-strong coupling regime, the quantum advantage of the QB's maximum charging power is the same as that of the Dicke QB, i.e., $\ensuremath{\alpha}=1.5$.