Ultrastrong Coupling Regime Research Articles

All-optical quantum simulation of ultrastrong optomechanics

The observation of single-photon optomechanical effects is a desired task in cavity optomechanics. However, the realization of ultrastrong optomechanical interaction remains a big challenge. Here, we present an all-optical scheme to simulate ultrastrong optomechanical coupling based on a Fredkin-type interaction, which consists of two exchange-coupled modes with the coupling strength depending on the photon number in another controller mode. This coupling enhancement is assisted by the displacement amplification according to the physical idea of the Bogoliubov approximation, which is realized by utilizing a strong driving to pump one of the two exchanging modes. Our numerical simulations demonstrate that the enhanced optomechanical coupling can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. We also show the creation of macroscopic quantum superposed states and the implementation of a weak-to-strong transition for quantum measurement in this system. This work will pave the way to quantum simulation of single-photon optomechanical effects with current experimental platforms.

Weak and Ultrastrong Coupling Limits of the Quantum Mean Force Gibbs State.

The Gibbs state is widely taken to be the equilibrium state of a system in contact with an environment at temperature T. However, non-negligible interactions between system and environment can give rise to an altered state. Here, we derive general expressions for this mean force Gibbs state, valid for any system that interacts with a bosonic reservoir. First, we derive the state in the weak coupling limit and find that, in general, it maintains coherences with respect to the bare system Hamiltonian. Second, we develop a new expansion method suited to investigate the ultrastrong coupling regime. This allows us to derive the explicit form for the mean force Gibbs state, and we find that it becomes diagonal in the basis set by the system-reservoir interaction instead of the system Hamiltonian. Several examples are discussed including a single qubit, a three-level V-system, and two coupled qubits all interacting with bosonic reservoirs. The results shed light on the presence of coherences in the strong coupling regime, and provide key tools for nanoscale thermodynamics investigations.

Strong interaction between two photons and a plasmon of a complementary metamaterial in a terahertz dual cavity

Guided by Babinet’s principle, we explore strong coupling between the effective magnetic dipole moments of complementary split-slotring metamaterials and the magnetic field of a cavity radiation mode. The strong coupling is demonstrated by a pronounced Rabi splitting of the cavity polariton resonances, corresponding to the ultrastrong coupling regime, with the metamaterial placed at a magnetic-field anti-node of the bare cavity radiation mode, where the corresponding electric field vanishes and no strong interaction was previously observed with a metamaterial consisting of electric dipole resonators. Moreover, exploiting the complementary bandpass/bandstop characteristics of the split-slotring resonators, we realize a dual cavity, coupled via the intermediate metamaterial, and observe strong interaction among two photons and the plasmon in the cavity. When the dual cavity is degenerate, the three-particle interaction collapses to an effective two-particle interaction, where the generalized Rabi splitting is increased by a factor of 2 compared to the single-cavity case involving only one photon and one plasmon. The experimental results are supported both by classical electromagnetic simulations and coupled-oscillator models adopted from cavity quantum electrodynamics.

Stabilization of product states and excited-state quantum phase transitions in a coupled qubit-field system

We study a system of a single qubit (or a few qubits) interacting with a soft-mode bosonic field. Considering an extended version of the Rabi model with both parity-conserving and parity-violating interactions, we disclose a complex arrangement of quantum phase transitions in the ground- and excited-state domains. An experimentally testable signature of some of these transitions is a dynamical stabilization of a fully factorized qubit-field state involving the field vacuum. It happens in the ultrastrong coupling regime where the superradiant field equilibrium is far from the vacuum state. The degree of stabilization varies abruptly with interaction parameters and increases with the softness of the field mode. We analyze semiclassical origins of these effects and show their connection to various forms of excited-state quantum phase transitions.

Tunable coupling of terahertz Dirac plasmons and phonons in transition-metal dichalcogenide-based van der Waals heterostructures

Dirac plasmons in graphene hybridize with phonons of transition metal dichalcogenides (TMDs) when the materials are combined in so-called van der Waals heterostructures (vdWh), thus forming surface plasmon-phonon polaritons (SPPPs). The extend to which these modes are coupled depends on the TMD composition and structure, but also on the plasmons’ properties. By performing realistic simulations that account for the contribution of each layer of the vdWh separately, we calculate how the strength of plasmon-phonon coupling depends on the number and composition of TMD layers, on the graphene Fermi energy and the specific phonon mode. From this, we present a semiclassical theory that is capable of capturing all relevant characteristics of the SPPPs. We find that it is possible to realize both strong and ultra-strong coupling regimes by tuning graphene’s Fermi energy and changing TMD layer number.

Transmission spectra of the driven, dissipative Rabi model in the ultrastrong-coupling regime

We present theoretical transmission spectra of a strongly driven, damped flux qubit coupled to a dissipative resonator in the ultrastrong-coupling regime. Such a qubit-oscillator system, described within a dissipative Rabi model, constitutes the building block of superconducting circuit QED platforms. The addition of a strong drive allows one to characterize the system properties and study novel phenomena, leading to a better understanding and control of the qubit-oscillator system. In this work, the calculated transmission of a weak probe field quantifies the response of the qubit, in frequency domain, under the influence of the quantized resonator and of the strong microwave drive. We find distinctive features of the entangled driven qubit-resonator spectrum, namely resonant features and avoided crossings, modified by the presence of the dissipative environment. The magnitude, positions, and broadening of these features are determined by the interplay among qubit-oscillator detuning, the strength of their coupling, the driving amplitude, and the interaction with the heat bath. This work establishes the theoretical basis for future experiments in the driven ultrastrong-coupling regime.

Vibrational Coupling of Water from Weak to Ultrastrong Coupling Regime via Cavity Mode Tuning

Vibrational strong coupling is an emerging method for modulation of ground-state molecular properties. Spectroscopic information about the vibrational coupling state is essential for determination ...

Distant emitters in ultrastrong waveguide QED: Ground-state properties and non-Markovian dynamics

Starting from the paradigmatic spin-boson model (SBM), we investigate the static and dynamical properties of a system of two distant two-level emitters coupled to a one-dimensional Ohmic waveguide beyond the rotating wave approximation. Employing static and dynamical polaron Ans\"atze we study the effects of finite separation distance on the behavior of the photon-mediated Ising-like interaction, qubit frequency renormalization, ground-state magnetization, and entanglement entropy of the two-qubit system. Based on previous works we derive an effective approximate Hamiltonian for the two-impurity SBM that preserves the excitation-number and thus facilitates the analytical treatment. In particular, it allows us to introduce non-Markovianity arising from delay-feedback effects in two distant emitters in the so-called ultrastrong coupling (USC) regime. We test our results with numerical simulations performed over a discretized circuit-QED model, finding perfect agreement with previous results, and showing interesting dynamical effects arising in ultrastrong waveguide QED with distant emitters. In particular, we revisit the Fermi two-atom problem showing that, in the USC regime, initial correlations yield two different evolutions for symmetric and antisymmetric states even before the emitters become causally connected. Finally, we demonstrate that the collective dynamics, e.g., superradiance or subradiance, are affected not only by the distance between emitters, but also by the coupling, due to significant frequency renormalization. This constitutes another dynamical consequence of the USC regime.

Ultrastrong Exciton-Photon Coupling in Broadband Solar Absorbers.

The recent development of organic polaritonic solar cells, in which sunlight absorbers and photon modes of a resonator are hybridized as a result of their strong coupling, has revealed the potential this interaction offers to control and enhance the performance of these devices. In this approach, the photovoltaic cell is built in such a way that it also behaves as an optical cavity supporting spectrally well-defined resonances, which match the broad absorption bands of the dyes employed. Herein we focus on the experimental and theoretical analysis of the specific spectral and angular optical absorption characteristics of a broadband light harvester, namely a subphthalocyanine, when operating in the ultrastrong coupling regime. We discuss the implications of having a broad distribution of oscillator strengths and demonstrate that rational design of the layered structure is needed to optimize both the spectral and the angular response of the sunlight harvester dye.

Unified Description of Saturation and Bistability of Intersubband Transitions in the Weak and Strong Light-Matter Coupling Regimes.

We propose a unified description of intersubband absorption saturation for quantum wells inserted in a resonator, both in the weak and strong light-matter coupling regimes. We demonstrate how absorption saturation can be engineered. In particular, we show that the saturation intensity increases linearly with the doping in the strong coupling regime, while it remains doping independent in weak coupling. Hence, countering intuition, the most suitable region to exploit low saturation intensities is not the ultrastrong coupling regime, but is instead at the onset of the strong light-matter coupling. We further derive explicit conditions for the emergence of bistability. This Letter sets the path toward, as yet, nonexistent ultrafast midinfrared semiconductor saturable absorption mirrors (SESAMs) and bistable systems. As an example, we show how to design a midinfrared SESAM with a 3 orders of magnitude reduction in saturation intensity, down to ≈5 kW cm^{-2}.

Robust Strong-Coupling Architecture in Circuit Quantum Electrodynamics

We report on a robust method to achieve strong coupling between a superconducting flux qubit and a high-quality quarter-wavelength coplanar waveguide resonator. We demonstrate the progression from the strong to ultrastrong coupling regime by varying the length of a shared inductive coupling element, ultimately achieving a qubit-resonator coupling strength of 655 MHz, $10\mathrm{%}$ of the resonator frequency. We derive an analytical expression for the coupling strength in terms of circuit parameters and also discuss the maximum achievable coupling within this framework. We experimentally characterize flux qubits coupled to superconducting resonators using one- and two-tone spectroscopy methods, demonstrating excellent agreement with the proposed theoretical model.

Lamb Shift and the Vacuum Rabi Splitting in a Strongly Dissipative Environment.

We study the vacuum Rabi splitting of a qubit ultrastrongly coupled to a high-Q cavity mode and a radiation reservoir. Three methods are employed: a numerically exact variational approach with a multiple Davydov ansatz, the rotating-wave approximation (RWA), and the transformed RWA. Agreement between the variational results and the transformed RWA results is found in the regime of validity of the latter, where the RWA breaks down completely. We illustrate that the Lamb shift plays an essential role in modifying the vacuum Rabi splitting in the ultrastrong coupling regime, leading to off-resonant qubit-cavity coupling even though the cavity frequency equals the bare transition frequency of the qubit. Specifically, the emission spectrum exhibits one broad low-frequency peak and one narrow high-frequency peak in the presence of relatively weak cavity-qubit coupling. As the cavity-qubit coupling increases, the low-frequency peak narrows while the high-frequency peak broadens until they have similar widths.

Strong light-matter coupling for optical switching through the fluorescence and FRET control

Resonant interaction between excitonic transitions of molecules and localized electromagnetic field forms the hybrid polaritonic states. Tuneable microresonators may change the light-matter coupling strength and modulate them from weak to strong and ultra-strong coupling regimes. In this work we have realised strong coupling between the tuneable open-access cavity mode and the excitonic transitions in oligonucleotide-based molecular beacons with their terminus labelled with a pair of organic dye molecules demonstrating an efficient donor-to-acceptor Förster resonance energy transfer (FRET). We show that the predominant strong coupling of the cavity photon to the exciton transition in the donor dye molecule can lead to such a large an energy shift that the energy transfer from the acceptor exciton reservoir to the mainly donor lower polaritonic state can be achieved, thus yielding the chromophores’ donor–acceptor role reversal or “carnival effect”. The data show the possibility for confined electromagnetic fields to control and mediate polariton-assisted remote energy transfer. Obtained results open the avenues to quantum optical switching and other applications.

Quantum simulation of tunable and ultrastrong mixed-optomechanics.

We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators.

Parity-Symmetry-Protected Multiphoton Bundle Emission.

We demonstrate symmetry protected multiphoton bundle emission in the cavity QED system under the ultrastrong coupling regime. Our proposal only enables the super-Rabi oscillations with periodic generation of even correlated photons in the cavity, which is realized by combining the laser driven flip of qubit and the symmetry conserved transitions induced by Rabi interaction with parity symmetry. Combined with dissipation, only 2n-photon bundle emissions are allowed, due to the almost perfect suppression of bundle emissions with odd correlated photons. Meanwhile, the corresponding purities are significantly enhanced by the parity symmetry. This work extends multiphoton bundle emission to the ultrastrong coupling regime, and offers the prospect of exploring symmetry-protected multiphoton physics.

Polaritonic nonlocality in light–matter interaction

Sub-wavelength electromagnetic field localization has been central in photonic research in the last decade, allowing to enhance sensing capabilities as well as increasing the coupling between photons and material excitations. The ultrastrong light-matter coupling regime in the THz range with split-ring resonators coupled to magnetoplasmons has been widely investigated, achieving successive world-records for the largest light-matter coupling ever achieved. Ever shrinking resonators have allowed to approach the regime of few electrons strong coupling, in which single-dipole properties can be modified by the vacuum field. Here we demonstrate, theoretically and experimentally, the existence of a limit to the possibility of arbitrarily increasing electromagnetic confinement in polaritonic systems. Strongly sub-wavelength fields can excite a continuum of high-momenta propagative magnetoplasmons. This leads to peculiar nonlocal polaritonic effects, as certain polaritonic features disappear and the system enters in the regime of bound-to-continuum strong coupling. Emerging nonlinearities due to the local breaking of Kohn's theorem are also reported.

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.