Vacuum Rabi Research Articles

Direct Microwave Spectroscopy of Andreev Bound States in Planar Ge Josephson Junctions

We demonstrate microwave measurements of the Andreev-bound-state (ABS) spectrum in planar Josephson junctions (JJs) defined in Ge high-mobility two-dimensional hole gases contacted by superconducting platinum germanosilicide (PtSiGe). The JJs and readout circuitry are located on separate chips and inductively coupled via flip-chip bonding. For a device with 350-nm junction length, the spectroscopic signatures were consistent with the short-junction limit, with an induced superconducting gap Δ∗≈48μeV and transmission τ≈0.94. The interaction between the highest-transmission ABS and the resonator was well described by a Jaynes-Cummings model with a vacuum Rabi splitting of approximately 6 MHz. A device with a junction length of 1μm showed an ABS spectrum consistent with a long-junction model. Time-resolved monitoring of the readout resonator in the dispersive regime revealed gate-voltage tunable-junction parity fluctuations on the time scale of seconds. Our work indicates a viable path toward hybrid quantum devices based on planar Ge. Published by the American Physical Society 2024

Tunable coupling of a quantum phononic resonator to a transmon qubit via galvanic-contact flip-chip architecture

A hybrid system with tunable coupling between phonons and qubits shows great potential for advancing quantum information processing. In this work, we demonstrate strong and tunable coupling between a surface acoustic wave resonator and a transmon qubit based on the galvanic-contact flip-chip technique. The coupling strength varies from 2π× 7.0 to −2π× 20.6 MHz, which is extracted from different vacuum Rabi oscillation frequencies. The phonon-induced ac Stark shift of the qubit at different coupling strengths is also shown. Our approach offers a good experimental platform for exploring quantum acoustics and hybrid systems.

Background-free imaging of cold atoms in optical traps

Optical traps, including those used in atomic physics, cold chemistry, and quantum science, are widely used in the research on cold atoms and molecules. Owing to their microscopic structure and excellent operational capability, optical traps have been proposed for cold atom experiments involving complex physical systems, which generally induce violent background scattering. In this study, using a background-free imaging scheme in cavity quantum electrodynamics systems, a cold atomic ensemble was accurately prepared below a fiber cavity and loaded into an optical trap for transfer into the cavity. By satisfying the demanding requirements for the background-free imaging scheme in optical traps, cold atoms in an optical trap were detected with a high signal-to-noise ratio while maintaining atomic loading. The cold atoms were then transferred into the fiber cavity using an optical trap, and the vacuum Rabi splitting was measured, facilitating relevant research on cavity quantum electrodynamics. This method can be extended to related experiments involving cold atoms and molecules in complex physical systems using optical traps.

Hybrid architectures for terahertz molecular polaritonics

Atoms and their different arrangements into molecules are nature’s building blocks. In a regime of strong coupling, matter hybridizes with light to modify physical and chemical properties, hence creating new building blocks that can be used for avant-garde technologies. However, this regime relies on the strong confinement of the optical field, which is technically challenging to achieve, especially at terahertz frequencies in the far-infrared region. Here we demonstrate several schemes of electromagnetic field confinement aimed at facilitating the collective coupling of a localized terahertz photonic mode to molecular vibrations. We observe an enhanced vacuum Rabi splitting of 200 GHz from a hybrid cavity architecture consisting of a plasmonic metasurface, coupled to glucose, and interfaced with a planar mirror. This enhanced light-matter interaction is found to emerge from the modified intracavity field of the cavity, leading to an enhanced zero-point electric field amplitude. Our study provides key insight into the design of polaritonic platforms with organic molecules to harvest the unique properties of hybrid light-matter states.

Strong coupling in molecular systems: a simple predictor employing routine optical measurements.

We provide a simple method that enables readily acquired experimental data to be used to predict whether or not a candidate molecular material may exhibit strong coupling. Specifically, we explore the relationship between the hybrid molecular/photonic (polaritonic) states and the bulk optical response of the molecular material. For a given material, this approach enables a prediction of the maximum extent of strong coupling (vacuum Rabi splitting), irrespective of the nature of the confined light field. We provide formulae for the upper limit of the splitting in terms of the molar absorption coefficient, the attenuation coefficient, the extinction coefficient (imaginary part of the refractive index) and the absorbance. To illustrate this approach, we provide a number of examples, and we also discuss some of the limitations of our approach.

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.

Topologically Protected Synthesizing of Fock States in a Circuit Quantum Electrodynamics Architecture

The preparation of Fock states is important for quantum information storage and processing. Herein, a two‐step protocol with topological protection for multi‐photon Fock states synthesizing in a circuit quantum electrodynamics (QED) architecture is presented. Due to photon number‐dependent vacuum Rabi splitting, the dynamics of the Jaynes–Cummings ladder in the resonant regime can be equivalent to a spin‐1/2 chain while a multi‐frequency microwave pulse is applied. Based on the topologically assisted quantum state transfer (QST)technique, multi‐photon Fock states can be conditionally generated. This method significantly reduces the complexity of experimental manipulation compared with previous multi‐step methods and is more robust as a result of topological protection. Furthermore, the protocol indicates that the circuit QED architecture could potentially provide a platform to explore the exotic phase in condensed matter.

Dynamic Fabry-Pérot cavity stabilization technique for atom-cavity experiments

We present a stabilization technique developed to lock and dynamically tune the resonant frequency of a moderate finesse Fabry-Pérot (FP) cavity used in precision atom-cavity quantum electrodynamics (QED) experiments. Most experimental setups with active stabilization either operate at one fixed resonant frequency or use transfer cavities to achieve the ability to tune the resonant frequency of the cavity. In this work, we present a simple and cost-effective solution to actively stabilize an optical cavity while achieving a dynamic tuning range of over 100 MHz with a precision under 1 MHz. Our unique scheme uses a reference laser locked to an electro-optic modulator (EOM) shifted saturation absorption spectroscopy (SAS) signal. The cavity is locked to the PDH error signal obtained from the dip in the reflected intensity of this reference laser. Our setup provides the feature to efficiently tune the resonant frequency of the cavity by only changing the EOM drive without unlocking and re-locking either the reference laser or the cavity. We present measurements of precision control of the resonant cavity frequency and vacuum Rabi splitting (VRS) to quantify the stability achieved and hence show that this technique is suitable for a variety of cavity QED experiments.

Sculpting ultrastrong light-matter coupling through spatial matter structuring.

The central theme of cavity quantum electrodynamics is the coupling of a single optical mode with a single matter excitation, leading to a doublet of cavity polaritons which govern the optical properties of the coupled structure. Especially in the ultrastrong coupling regime, where the ratio of the vacuum Rabi frequency and the quasi-resonant carrier frequency of light, ΩR/ω c, approaches unity, the polariton doublet bridges a large spectral bandwidth 2ΩR, and further interactions with off-resonant light and matter modes may occur. The resulting multi-mode coupling has recently attracted attention owing to the additional degrees of freedom for designing light-matter coupled resonances, despite added complexity. Here, we experimentally implement a novel strategy to sculpt ultrastrong multi-mode coupling by tailoring the spatial overlap of multiple modes of planar metallic THz resonators and the cyclotron resonances of Landau-quantized two-dimensional electrons, on subwavelength scales. We show that similarly to the selection rules of classical optics, this allows us to suppress or enhance certain coupling pathways and to control the number of light-matter coupled modes, their octave-spanning frequency spectra, and their response to magnetic tuning. This offers novel pathways for controlling dissipation, tailoring quantum light sources, nonlinearities, correlations as well as entanglement in quantum information processing.

Terahertz Cavity Magnon Polaritons

AbstractHybrid light–matter coupled states, or polaritons, in magnetic materials have attracted significant attention due to their potential for enabling novel applications in spintronics and quantum information processing. However, most magnon‐polariton studies in the strong coupling regime to date have been carried out for ferromagnetic materials with magnon excitations at gigahertz frequencies. Here, strong resonant photon–magnon coupling at frequencies above 1 terahertz is investigated for the first time in a prototypical room‐temperature antiferromagnetic insulator, NiO, inside a Fabry–Pérot cavity. The cavity is formed by the crystal itself with a thickness adjusted to an optimal value. Terahertz time‐domain spectroscopy measurements in magnetic fields up to 25 T reveal the evolution of the magnon frequency through Fabry–Pérot cavity modes with photon–magnon anticrossing behavior, demonstrating clear vacuum Rabi splittings exceeding the polariton linewidths. These results show that NiO is a promising platform for exploring antiferromagnetic spintronics and cavity magnonics in the terahertz frequency range.

Continuous-wave and pulsed EPR studies of glass-like carbon with high spin concentration: Evidence for triplet states

Glass-like carbons (GLCs) are a large group of disordered carbon materials which have applications in various fields, but not all their properties are well characterized. In particular, they have high concentration of paramagnetic centers (PCs) which are easily observed by electron paramagnetic resonance (EPR). However, an apparently simple EPR spectrum, together with its peculiarities caused by high electrical conductivity, make it difficult to identify the PCs and their origin remains unknown. To resolve these unsettled questions, in this work we use the vacuum Rabi splitting and Rabi oscillations which so far have not been applied to study these materials by the continuous wave (CW) and pulsed EPR. GLC produced by pyrolysis of phenol-formaldehyde resin at 1120 K was studied in the temperature range of 4.3–300 K. Using the Rabi splitting we found conditions for undistorted registration of CW EPR spectra and determined spin concentration (1×1020 spin/g). The temperature dependence of the EPR susceptibility shows the coexistence of Pauli paramagnetism due to conduction electrons and the Curie-type paramagnetism of thermally activated PCs with the activation energy of 5.7 cm-1. These PCs may be excited triplet states, the presence of which is revealed by Rabi oscillations in the pulsed EPR.

Stochastic Approach to the Quantum Noise of a Single-Emitter Nanolaser.

It is shown that the quantum intensity noise of a single-emitter nanolaser can be accurately computed by adopting a stochastic interpretation of the standard rate equation model. The only assumption made is that the emitter excitation and photon number are stochastic variables with integer values. This extends the validity of rate equations beyond the mean-field limit and avoids using the standard Langevin approach, which is shown to fail for few emitters. The model is validated by comparison to full quantum simulations of the relative intensity noise and second-order intensity correlation function, g^{(2)}(0). Surprisingly, even when the full quantum model displays vacuum Rabi oscillations, which are not accounted for by rate equations, the intensity quantum noise is correctly predicted by the stochastic approach. Adopting a simple discretization of the emitter and photon populations, thus, goes a long way in describing quantum noise in lasers. Besides providing a versatile and easy-to-use tool for modeling emerging nanolasers, these results provide insight into the fundamental nature of quantum noise in lasers.

Optical Spectra of Plasmon–Exciton Core–Shell Nanoparticles: A Heuristic Quantum Approach

Light–matter coupling in plasmonic nanocavities has been widely studied in the past years. Yet, for core–shell particles, popular electromagnetic models that use the classical Lorentz oscillator to describe the shell predict extinction spectra with three maxima, if the plasmon and the shell absorption are in resonance. In contrast, experiments exhibit only two peaks, as also expected from simple quantum models of hybrid states. In order to reconcile the convenient and widely used classical electromagnetic description with experimental data, we connect it to the quantum world by conceiving a heuristic quantum model. Our model is based on the permittivity of a two-level system in a classical electric field derived from the optical Bloch equations. The light–matter coupling is included via the collective vacuum Rabi frequency Ω0. Using our model, we obtain excellent agreement with a series of experimental extinction spectra of particles with various coupling strengths due to a systematic size variation. The suppression of the third maximum, which mainly stems from the absorption in the shell, can be interpreted as a vacuum induced power broadening, which may occur in lossy (plasmonic) cavities below the strong-coupling regime.

On the Dynamics of the Tavis–Cummings Model

The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems (TLSs) that are collectively coupled to a common cavity resonator. The associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including $\sqrt{N}$- scaling, dark states, bright states, single-excitation superradiant and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in Tavis-Cummings systems. On the basis of the linear model, an analytic form is presented for the steady-state output state of the Tavis-Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis-Cummings model in the multi-excitation scenario. Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis-Cummings model, which is applicable to the multi-excitation case.

Exciton polariton interactions in Van der Waals superlattices at room temperature

Monolayer transition-metal dichalcogenide (TMD) materials have attracted a great attention because of their unique properties and promising applications in integrated optoelectronic devices. Being layered materials, they can be stacked vertically to fabricate artificial van der Waals lattices, which offer unique opportunities to tailor the electronic and optical properties. The integration of TMD heterostructures in planar microcavities working in strong coupling regime is particularly important to control the light-matter interactions and form robust polaritons, highly sought for room temperature applications. Here, we demonstrate the systematic control of the coupling-strength by embedding multiple WS2 monolayers in a planar microcavity. The vacuum Rabi splitting is enhanced from 36 meV for one monolayer up to 72 meV for the four-monolayer microcavity. In addition, carrying out time-resolved pump-probe experiments at room temperature we demonstrate the nature of polariton interactions which are dominated by phase space filling effects. Furthermore, we also observe the presence of long-living dark excitations in the multiple monolayer superlattices. Our results pave the way for the realization of polaritonic devices based on planar microcavities embedding multiple monolayers and could potentially lead the way for future devices towards the exploitation of interaction-driven phenomena at room temperature.

Vacuum Rabi Splitting and Kerr Effect of a Hybrid Spin–Magnon–Photon System

AbstractThe vacuum Rabi splitting and Kerr effect are investigated theoretically in a hybrid spin–magnon–photon system, where the nitrogen‐vacancy center in diamond driven by two light fields is coupled to a spherical micromagnet embedded in a superconducting coplanar waveguide resonator. The results indicate that the phenomenon of the Mollow triplet and vacuum Rabi splitting can appear by controlling the spin–magnon coupling and magnon–photon coupling. It is shown that the probe absorption spectrum can be adjusted effectively via the pump frequency detuning. Moreover, it is demonstrated that the optical Kerr effect can be tuned by changing the Rabi frequency. This work may provide a possibility for the applications in quantum information processing and quantum sensing of magnetic signal.

Positronium density measurements using polaritonic effects

Recent experimental advances in Positronium (Ps) physics have made it possible to produce dense Ps ensembles in which Ps-Ps interactions may occur, leading to the production of Ps$_2$ molecules and paving the way to the realization of a Ps Bose-Einstein Condensate (BEC). In order to achieve this latter goal it would be advantageous to develop new methods to measure Ps densities in real-time. Here we describe a possible approach to do this using polaritonic methods: using realistic experimental parameters we demonstrate that a dense Ps gas can be strongly coupled to the photonic field of a distributed Bragg reflector microcavity. In this strongly coupled regime, the optical spectrum of the system is composed of two hybrid positronium-polariton resonances separated by the vacuum Rabi splitting, which is proportional to the square root of the Ps density. Given that polaritons can be created on a sub-cycle timescale, a spectroscopic measurement of the vacuum Rabi splitting could be used as an ultra-fast Ps density measurement in regimes relevant to Ps BEC formation. Moreover, we show how positronium-polaritons could potentially enter the ultrastrong light-matter coupling regime, introducing a radically novel platform to explore its non-perturbative phenomenology.

Trapping of single atom and precise control of its coupling strength in micro-optical cavity

Cavity quantum electrodynamic system with strongly coupled single atoms provides a good platform for studying quantum information processing, quantum simulation, quantum network, and distributed quantum computing. Cooling and trapping single atoms is a crucial technique in the quantum technology. At present, in a high-finesse cavity with finite space, cooling and trapping single atoms is a big challenge, even though it is a mature technique for free space. Great efforts have been made to cool and trap single atoms inside a cavity, and for a trapped atom its lifetime has reached as long as tens of seconds. Developing a more flexible method of cooling and trapping single atoms in a cavity is still essential for a strongly coupled cavity quantum electrodynamic system. In this work, we demonstrate experimentally that a single cesium atom in a cavity can be trapped by utilizing a single optical tweezer settled in cavity mode, and its lifetime is (2.60 ± 0.18) s. The experiment is carried out in a Fabry-Perot cavity, which is assembled by two concave mirrors each with a curvature radius of 100 mm, and cavity length of 335 μm. The concave surfaces are highly reflective, and the cavity has a finesse of 6.1 × 10<sup>4</sup>. The 1080 nm optical tweezer with a waist of 2 μm is formed by an achromatic lens group with a numerical aperture of 0.4. At first, the precooled atomic assemble released from the magneto-optical trap (MOT) is transferred into cavity mode by an optical dipole trap with a waist of 36 μm. Then, one of the successfully transferred atoms is captured by the optical tweezer with the aid of cavity cooling mechanism. A blue detuned cavity locking laser is used as a standing-wave optical trap along the cavity axis. The signal of successfully trapped one atom is obtained by recording transmission of the cavity that will decrease owing to the strong coupling induced vacuum Rabi splitting. Finally, we demonstrate the precise manipulation of the atom-cavity coupling strength, which is achieved by scanning the position of the trapped atom step by step by using a high-precision translation stage. The system realized in this work can be used to study the dynamics of single atom-photon interactions with adjustable coupling strength. In addition, the mechanism adopted in this work is compatible with constructing tweezer arrays inside cavity mode, and thus possesses more flexibility and great potentials in cavity-based quantum entanglement and quantum simulation.

Molecular polariton electroabsorption

We investigate electroabsorption (EA) in organic semiconductor microcavities to understand whether strong light-matter coupling non-trivially alters their nonlinear optical [{chi }^{(3)}left(omega,{{{{mathrm{0,0}}}}}right)] response. Focusing on strongly-absorbing squaraine (SQ) molecules dispersed in a wide-gap host matrix, we find that classical transfer matrix modeling accurately captures the EA response of low concentration SQ microcavities with a vacuum Rabi splitting of hslash Omega approx 200 meV, but fails for high concentration cavities with hslash Omega approx 420 meV. Rather than new physics in the ultrastrong coupling regime, however, we attribute the discrepancy at high SQ concentration to a nearly dark H-aggregate state below the SQ exciton transition, which goes undetected in the optical constant dispersion on which the transfer matrix model is based, but nonetheless interacts with and enhances the EA response of the lower polariton mode. These results indicate that strong coupling can be used to manipulate EA (and presumably other optical nonlinearities) from organic microcavities by controlling the energy of polariton modes relative to other states in the system, but it does not alter the intrinsic optical nonlinearity of the organic semiconductor inside the cavity.

Strong optical coupling in metallo-dielectric hybrid metasurfaces.

Metasurfaces consisting of hybrid metal/dielectric nanostructures carry advantages of both material platforms. The hybrid structures can not only confine electromagnetic fields in subwavelength regions, but they may also lower the absorption losses. Such optical characteristics are difficult to realize in metamaterials with only metal or dielectric structures. Hybrid designs also expand the scope of material choices and the types of optical modes that can be excited in a metasurface, thereby allowing novel light matter interactions. Here, we present a metallo-dielectric hybrid metasurface design consisting of a high-index dielectric (silicon) nanodisk array on top of a metal layer (aluminum) separated by a buffer oxide (silica) layer. The dimensions of Si nanodisks are tuned to support anapole states and the period of the nanodisk array is designed to excite surface plasmon polariton (SPP) at the metal-buffer oxide interface. The physical dimensions of the Si nanodisk and the array periods are optimized to excite the anapole and the SPP at normal incidence of light in the visible-NIR (400-900 nm) wavelength range. Finite difference time domain (FDTD) simulations show that, when the nanodisk grating is placed at a specific height (∼200 nm) from the metal surface, the two modes strongly couple at zero detuning of the resonances. The strong coupling is evident from the avoided crossing of the modes observed in the reflectance spectra and in the spectral profile of light absorption inside the Si nanodisk. A vacuum Rabi splitting of up to ∼ 129 meV is achievable by optimizing the diameters of Si nanodisk and the nanodisk array grating period. The proposed metasurface design is promising to realize open cavity strongly coupled optical systems operating at room temperatures.