Ultrastrong Coupling Regime Research Articles

Proposal for a Nanomechanical Qubit

Mechanical oscillators have been demonstrated with very high quality factors over a wide range of frequencies. These also couple to a wide variety of fields and forces, making them ideal as sensors. The realization of a mechanically-based quantum bit could therefore provide an important new platform for quantum computation and sensing. Here we show that by coupling one of the flexural modes of a suspended carbon nanotube to the charge states of a double quantum dot defined in the nanotube, it is possible to induce sufficient anharmonicity in the mechanical oscillator so that the coupled system can be used as a mechanical quantum bit. This can however only be achieved when the device enters the ultrastrong coupling regime. We discuss the conditions for the anharmonicity to appear, and we show that the Hamiltonian can be mapped onto an anharmonic oscillator, allowing us to work out the energy level structure and how decoherence from the quantum dot and the mechanical oscillator are inherited by the qubit. Remarkably, the dephasing due to the quantum dot is expected to be reduced by several orders of magnitude in the coupled system. We outline qubit control, readout protocols, the realization of a CNOT gate by coupling two qubits to microwave cavity, and finally how the qubit can be used as a static force quantum sensor.

Resonant Raman scattering of single molecules under simultaneous strong cavity coupling and ultrastrong optomechanical coupling in plasmonic resonators: Phonon-dressed polaritons

Plasmonic dimer cavities can induce extreme electric-field hot spots that allow one to access ultrastrong coupling regimes using Raman-type spectroscopy on single vibrating molecules. Using a generalized master equation, we study resonant Raman scattering in the strong coupling regime of cavity quantum electrodynamics, when also in the vibrational ultrastrong coupling regime, leading to ``phonon-dressed polaritons.'' The master equation rigorously includes spectral baths for the cavity and vibrational degrees of freedom, as well as a pure dephasing bath for the resonant two-level system, which play a significant role. Employing realistic parameters for gold dimer cavity modes, we investigate the emission spectra in several characteristic strong coupling regimes, leading to extremely rich spectral resonances due to an interplay of phonon-modified polariton states and bath-induced resonances. We also show explicitly the failure of the standard master equation in these quantum nonlinear regimes.

One-Photon Solutions to the Multiqubit Multimode Quantum Rabi Model for Fast W-State Generation.

General solutions to the quantum Rabi model involve subspaces with an unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for an arbitrary number of qubits and photon modes. Such solutions exist for arbitrary single qubit-photon coupling strength with constant eigenenergy, while still being qubit-photon entangled states. Taking advantage of their peculiarities and the reach of the ultrastrong coupling regime, we propose an adiabatic scheme for the fast and deterministic generation of a two-qubit Bell state and arbitrary single-photon multimode W states with nonadiabatic error less than 1%. Finally, we propose a superconducting circuit design to catch and release the W states, and shows the experimental feasibility of the multimode multiqubit quantum Rabi model.

Water Oxidation under Modal Ultrastrong Coupling Conditions Using Gold/Silver Alloy Nanoparticles and Fabry–Pérot Nanocavities

AbstractWe developed a photoanode consisting of Au‐Ag alloy nanoparticles (NPs), a TiO2 thin film and a Au film (AATA) under modal strong coupling conditions with a large splitting energy of 520 meV, which can be categorized into the ultrastrong coupling regime. We fabricated a photoanode under ultrastrong coupling conditions to verify the relationship between the coupling strength and photoelectric conversion efficiency and successfully performed efficient photochemical reactions. The AATA photoanode showed a 4.0 % maximum incident photon‐to‐current efficiency (IPCE), obtained at 580 nm, and the internal quantum efficiency (IQE) was 4.1 %. These results were attributed to the high hot‐electron injection efficiency due to the larger near‐field enhancement and relatively negative potential distribution of the hot electrons. Furthermore, hybrid mode‐induced water oxidation using AATA structures was performed, with a Faraday efficiency of more than 70 % for O2 evolution.

Strong exciton−photon coupling with colloidal quantum dots in a tunable microcavity

Polariton emission from optical cavities integrated with various luminophores has been extensively studied recently due to the wide variety of possible applications in photonics, particularly promising in terms of the fabrication of low-threshold sources of coherent emission. Tunable microcavities allow extensive investigation of the photophysical properties of matter placed inside the cavity by deterministically changing the coupling strength and controllable switching from weak to strong and ultra-strong coupling regimes. Here, we demonstrate room-temperature strong coupling of exciton transitions in CdSe/ZnS/CdS/ZnS colloidal quantum dots with the optical modes of a tunable low-mode-volume microcavity. Strong coupling is evidenced by a large Rabi splitting of the photoluminescence spectra depending on the detuning of the microcavity. A coupling strength of 154 meV has been achieved. High quantum yields, excellent photostability, and scalability of fabrication of quantum dots (QDs) pave the way to practical applications of coupled systems based on colloidal QDs in photonics, optoelectronics, and sensing.

Plasmon polaritons in nanoparticle supercrystals: Microscopic quantum theory beyond the dipole approximation

Crystals of plasmonic metal nanoparticles have intriguing optical properties. They reach the regimes of ultrastrong and deep strong light-matter coupling, where the photonic states need to be included in the simulation of material properties. We propose a quantum description of the plasmon polaritons in supercrystals that starts from the dipole and quadrupole excitations of the nanoparticle building blocks and their coupling to photons. Our model excellently reproduces results of finite difference time domain simulations. It provides detailed insight into the emergence of the polariton states. Using the example of a face centered cubic crystals we show that the dipole and quadrupole states mix in many high symmetry directions of the Brilouin zone. A proper description of the plasmon and plasmon-polariton band structure is only possible when including the quadrupole-derived states. Our model leads to an expression of the reduced coupling strength in nanoparticle supercrystals that we show to enter the deep strong coupling regime for metal fill fractions above $0.8$. In addition to the plasmon-polariton energies we analyse the relative contributions of the dipole, quadrupole, and photonic states to their eigenfunctions and are able to demonstrate the decoupling of light in the deep strong coupling regime. Our results pave the way for a better understanding of the quantum properties of metallic nanoparticle supercrystals in the ultrastrong and deep-strong coupling regime.

Generalized spin kitten states in a strongly coupled spin-oscillator system

Utilizing an adiabatic approximation method, a bipartite qudit-oscillator Hamiltonian is studied for low-spin values in both strong and ultrastrong coupling regimes. The quasiprobability densities on the hybrid factorized phase space are introduced. Integrating over a sector of the composite phase space, the quasiprobability distributions of its complementary subsystem are recovered. In the strong coupling regime, the qudit entropy displays a pattern of quasiperiodic collapses and revivals, where the latter coincide with locally minimum entropy configurations. Starting with a bipartite factorizable initial state, we observe that almost pure spin kitten type states dynamically develop at near-null values of entropy. The Hilbert-Schmidt distance measure of these states puts them metrically far away from the initial state. Other localized spin states form at locally minimum but significantly large values of entropy. The evolution to the nonclassical transitory spin states is displayed via the diagonal spin ${\mathrm{P}}_{\mathcal{Q}}$ representation. As another manifestation of nonclassicality the emergence of the spin-squeezed states during the bipartite evolution is observed. In the ultrastrong coupling domain, a large number of interaction-dependent modes and their harmonics are generated. The consequent randomization of the phases eliminates the quasiperiodicity of the system which is now driven towards a stabilization of the entropy that also undergoes stochastic fluctuations around a suitably stabilized value. In both the strong and ultrastrong coupling realms, antibunching of the photoemission events is realized particularly for the small spin values.

Strong Coupling of an Fe - Co Alloy with Ultralow Damping to Superconducting Co-planar Waveguide Resonators

We report on the strong coupling between a metallic ferromagnetic Fe75Co25 thin film patterned element and a range of superconducting Nb half-wavelength co-planar waveguide (CPW) resonators. By varying the volume of the ferromagnet we demonstrate that the coupling rate scales linearly with the square root of the number of spins and achieve a coupling rate over 700 MHz, approaching the ultrastrong coupling regime. Experiments varying the center conductor width while maintaining constant magnetic volume verify that decreasing the center conductor width increases coupling and cooperativity. Our results show that the frequency dependence of the coupling rate is linear with the fundamental and higher order odd harmonics of the CPW, but with differing efficiencies. The results show promise for scaling planar superconducting resonator/magnetic hybrid systems to smaller dimensions.

Gauge principle and gauge invariance in two-level systems

The quantum Rabi model is a widespread description of the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when the light-matter interaction reaches the so-called ultrastrong coupling regime. Recently, a modified quantum Rabi model able to provide gauge-invariant physical results (e.g., energy levels, expectation values of observables, quantum probabilities) in any interaction regime was introduced [Nature Physics 15, 803 (2019)]. Here we provide an alternative derivation of this result, based on the implementation in two-state systems of the gauge principle, which is the principle from which all the fundamental interactions in quantum field theory are derived. The adopted procedure can be regarded as the two-site version of the general method used to implement the gauge principle in lattice gauge theories. Applying this method, we also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multi-mode gauge-invariant quantum Rabi model beyond the dipole approximation.

Gauge freedom, quantum measurements, and time-dependent interactions in cavity QED

The interaction between the electromagnetic field inside a cavity and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies. Recently, new regimes beyond the weak and strong light-matter coupling have been explored in several settings. These regimes, where the interaction strength is comparable (ultrastrong) or even higher (deep-strong) than the transition frequencies in the system, can give rise to new physical effects and applications. At the same time, they challenge our understanding of cavity QED. When the interaction strength is so high, fundamental issues like the proper definition of subsystems and of their quantum measurements, the structure of light-matter ground states, or the analysis of time-dependent interactions are subject to ambiguities leading to even qualitatively distinct predictions. The resolution of these ambiguities is also important for understanding and designing next-generation quantum devices that will exploit the ultrastrong coupling regime. Here we discuss and provide solutions to these issues.

Elliptical rotation of a bosonic oscillator in ultrastrong waveguide QED

We investigate optical response of a linear waveguide quantum electrodynamics (QED) system, namely, an optical cavity coupled to a waveguide. Our analysis is based on exact diagonalization of the overall Hamiltonian and is therefore rigorous even in the ultrastrong coupling regime of waveguide QED. Owing to the counter-rotating terms in the cavity-waveguide coupling, the motion of cavity amplitude in the phase space is elliptical in general. Such elliptical motion becomes remarkable in the ultrastrong coupling regime due to the large Lamb shift comparable to the bare cavity frequency. We also reveal that such elliptical motion does not propagate into the output field and present an analytic form of the reflection coefficient that is asymmetric with respect to the resonance frequency.

Mapping the Cavity Optomechanical Interaction with Subwavelength-Sized Ultrasensitive Nanomechanical Force Sensors

In a canonical optomechanical system, mechanical vibrations are dynamically encoded on an optical probe field which reciprocally exerts a backaction force. Due to the weak single photon coupling strength achieved with macroscopic oscillators, most of existing experiments were conducted with large photon numbers to achieve sizeable effects, thereby causing a dilution of the original optomechanical non-linearity. Here, we investigate the optomechanical interaction of an ultrasensitive suspended nanowire inserted in a fiber-based microcavity mode. This implementation allows to enter far into the hitherto unexplored ultrastrong optomechanical coupling regime, where one single intracavity photon can displace the oscillator by more than its zero point fluctuations. To fully characterize our system, we implement nanowire-based scanning probe measurements to map the vectorial optomechanical coupling strength, but also to reveal the intracavity optomechanical force field experienced by the nanowire. This work establishes that the single photon cavity optomechanics regime is within experimental reach.

Understanding radiative transitions and relaxation pathways in plexcitons

Summary Molecular aggregates on plasmonic nanoparticles have emerged as attractive systems for the studies of polaritonic light-matter states, called plexcitons. Such systems are tunable, scalable, easy to synthesize, and offer sub-wavelength confinement, all while giving access to the ultrastrong light-matter coupling regime, promising a plethora of applications. However, the complexity of these materials prevented the understanding of their excitation and relaxation phenomena. Here, we follow the relaxation pathways in plexcitons and conclude that while the metal destroys the optical coherence, the molecular aggregate coupled to surface processes significantly contributes to the energy dissipation. We use two-dimensional electronic spectroscopy with theoretical modeling to assign the different relaxation processes to either molecules or metal nanoparticle. We show that the dynamics beyond a few femtoseconds has to be considered in the language of hot electron distributions instead of the accepted lower and upper polariton branches and establish the framework for further understanding.

Strong magnon–magnon coupling in synthetic antiferromagnets

A synthetic antiferromagnet, composed of two ferromagnetic layers separated by a non-magnetic layer, possesses two uniform precession resonance modes: in-phase acoustic mode and out-of-phase optic mode. In this work, we theoretically and numerically demonstrated the strong coupling between acoustic and optic magnon modes. The strong coupling is attributed to the symmetry breaking of the system, which can be realized by tilting the bias field or constructing an asymmetrical synthetic antiferromagnet. It is found that the coupling strength can be highly adjusted by tuning the tilting angle of bias field, the magnitude of antiferromagnetic interlayer exchange coupling, and the thicknesses of ferromagnetic layers. Furthermore, the coupling between acoustic and optic magnon modes can even reach the ultrastrong coupling regime. Our findings show high promise for investigating the quantum phenomenon with a magnonic platform.

Ground state properties and infrared spectra of anharmonic vibrational polaritons of small molecules in cavities.

Recent experiments and theory suggest that ground state properties and reactivity of molecules can be modified when placed inside a nanoscale cavity, giving rise to strong coupling between vibrational modes and the quantized cavity field. This is commonly thought to be caused either by a cavity-distorted Born-Oppenheimer ground state potential or by the formation of light-matter hybrid states, vibrational polaritons. Here, we systematically study the effect of a cavity on ground state properties and infrared spectra of single molecules, considering vibration-cavity coupling strengths from zero up to the vibrational ultrastrong coupling regime. Using single-mode models for Li-H and O-H stretch modes and for the NH3 inversion mode, respectively, a single cavity mode in resonance with vibrational transitions is coupled to position-dependent molecular dipole functions. We address the influence of the cavity mode on polariton ground state energies, equilibrium bond lengths, dissociation energies, activation energies for isomerization, and on vibro-polaritonic infrared spectra. In agreement with earlier work, we observe all mentioned properties being strongly affected by the cavity, but only if the dipole self-energy contribution in the interaction Hamiltonian is neglected. When this term is included, these properties do not depend significantly on the coupling anymore. Vibro-polaritonic infrared spectra, in contrast, are always affected by the cavity mode due to the formation of excited vibrational polaritons. It is argued that the quantized nature of vibrational polaritons is key to not only interpreting molecular spectra in cavities but also understanding the experimentally observed modification of molecular reactivity in cavities.

Polar diatomic molecules in optical cavities: Photon scaling, rotational effects, and comparison with classical fields.

We address topics related to molecules coupled to quantum radiation. The formalism of light-matter interaction is different for classical and quantum fields, but some analogies remain, such as the formation of light induced crossings. We show that under particular circumstances, the molecular dynamics under quantum or classical fields produce similar results, as long as the radiation is prepared as a Fock state and far from ultra-strong coupling regimes. At this point, the choice of specific initial Fock states is irrelevant since the dynamics scales. However, in realistic multistate molecular systems, radiative scaling may fail due to the presence of simultaneous efficient non-radiative couplings in the dynamics. Polar molecules have permanent dipoles, and within the context of the full quantum Rabi model with a Pauli-Fierz Hamiltonian, they play a crucial role in the polaritonic dynamics since both permanent dipole moments and self-energy terms produce drastic changes on the undressed potential energy surfaces at high coupling strengths. We also gauge the effect of including rotational degrees of freedom in cavity molecular photodynamics. For diatomic molecules, the addition of rotation amounts to transform (both with classical or quantum fields) a light induced crossing into a light induced conical intersection. However, we show that conical intersections due to molecular rotation do not represent the standard properties of well-known efficient intrinsic conical intersections inasmuch they do not enhance the quantum transition rates.

Ground state of a cross-cavity quantum Rabi model

We study a cross-cavity quantum Rabi model with ultrastrong coupling, and its analytical ground state is demonstrated to be approximately obtained by using the rotating-transformation method. Our method requires making three unitary transformations to the original Hamiltonian and ignoring the three-party cross interaction. In near-resonance and ultrastrong-coupling regimes, the ground-state fidelity is higher than 99% for a ±20% detuning range. We analytically demonstrate that the entanglement in ground state first quadratically increases with the qubit-oscillator coupling strength, then gets close to the maximum value 1. The oscillator’s nonclassical property in the ground state is well explained by analytically solving the Wigner function.

Avoiding gauge ambiguities in cavity quantum electrodynamics

Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few low-lying energy eigenstates. This effect is particularly prominent in the ultra-strong coupling regime. Such ambiguities arise because transformations reshuffle the partition between light and matter degrees of freedom and so level truncation is a gauge dependent approximation. To avoid this gauge ambiguity, we redefine the electromagnetic fields in terms of potentials for which the resulting canonical momenta and Hamiltonian are explicitly unchanged by the gauge choice of this theory. Instead the light/matter partition is assigned by the intuitive choice of separating an electric field between displacement and polarisation contributions. This approach is an attractive choice in typical cavity quantum electrodynamics situations.

Probing the spectrum of the Jaynes-Cummings-Rabi model by its isomorphism to an atom inside a parametric amplifier cavity

We show how the Jaynes--Cummings--Rabi model of cavity quantum electrodynamics can be realized via an isomorphism to the Hamiltonian of a qubit inside a parametric amplifier cavity. This realization clears the way to observe the full spectrum of the Rabi model via a probe applied to a parametric amplifier cavity containing a qubit and a parametric oscillator operating below threshold. An important outcome of the isomorphism is that the actual frequencies are replaced by detunings which make it feasible to reach the ultra-strong coupling regime. We find that inside this regime the probed spectrum displays a narrow resonance peak that is traced back to the transition between ground and first excited states. The exact form of these states is given at an energy crossing and then extended numerically. At the crossing, the eigenstates are entangled states of field and atom where the field is found inside squeezed cat states.

General solution of the time evolution of two interacting harmonic oscillators

We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry. In particular, we use this result to completely characterize the dynamics of the two oscillators interacting in the ultrastrong coupling regime with additional single-mode squeezing on both oscillators, as well as higher order terms. Furthermore, we compute quantities of interest, such as the average number of excitations and the correlations that are established between the two subsystems due to the evolution. We find that this model predicts a second order phase transition and we compute the critical exponents and the critical value. We also provide an exact decoupling of the time evolution in terms of simple quantum optical operations, which can be used for practical implementations and studies. Finally, we show how our techniques can be extended to include more oscillators and higher order interactions.