We present an ideal realization of the Tavis-Cummings model in the absence of atom number and coupling fluctuations by embedding a discrete number of fully controllable superconducting qubits at fixed positions into a transmission line resonator. Measuring the vacuum Rabi mode splitting with one, two and three qubits strongly coupled to the cavity field, we explore both bright and dark dressed collective multi-qubit states and observe the discrete square root of N scaling of the collective dipole coupling strength. Our experiments demonstrate a novel approach to explore collective states, such as the W-state, in a fully globally and locally controllable quantum system. Our scalable approach is interesting for solid-state quantum information processing and for fundamental multi-atom quantum optics experiments with fixed atom numbers.
We show that a set of N identical qubits coupled to a single cavity resonator can be decomposed into a set of independent subsystems, which can be thought of as higher pseudospin generalisations of the Jaynes-Cummings model. We derive and analyse the solutions to the equations of motion and demonstrate unusual beating behaviour resulting from a new form of square-root-n-type non-linearity appearing within a pseudospin ladder. Furthermore, we propose a relative phase shift transformation which allows one to switch/initiate the multi-qubit state in a desired pseudospin configuration, and show ho…
Qubit-qubit interactions can significantly boost quantum coherence times for Bell states. The coherence-time-enhancements are however not monotonic and there exists a phase where further increasing the interaction is unhelpful. A resonator in a suggested circuit QED type implementation of the Tavis-Cummings(Dicke) model, is shown to shift this transition point depending on the number of loaded photons. This allows the resonator to amplify the coherence enhancements in certain regimes. The interactions also induce unusual collapse and revival type behavior for the entanglement dynamics. A new a…
The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton-polarons is subject of ongoing debate. Here, we use an analogy to the Tavis-Cummings model of quantum optics to show that an exciton-polaron can be understood as a hybrid quasiparticle -- a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy An…
We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well known special functions. In the new form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. We also reveal connection between DTCM and …
The Tavis-Cummings model (the Dicke model treated in the rotating wave approximation) describing many two-level systems coupled to a single bosonic mode, has been long known to show collective semiclassical oscillations when prepared in an inverted state, with all two-level systems excited, and the bosonic mode empty. This paper discusses how the quantum dynamics approaches this semiclassical result for large numbers of two-level systems, focussing on how the eigenvalues approach their semiclassical limit. The approach to the semiclassical result is found to be slow, scaling like a power of th…
We numerically solve the Liouville equation for the Tavis Cummings model of multiple spins coupled to a lossless single mode cavity, starting from an initial condition with small numbers of fully polarized spins tipped by a specified angle, and the cavity in its ground Fock state. Time evolution of the magnetizations and cavity states, following small to medium nutation by a classical field, yields a microscopic quantum mechanical picture of radiation damping in magnetic resonance, and the formation of the free induction signal, that is, the transfer of Zeeman energy, via spin coherence, to ca…
Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light-matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis-Cummings (TC) model, in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excita…
Accidental Symmetry in the Tavis-Cummings Model via the Schwinger Boson Representation
Duke Quantum Center and Department of Physics, Duke University（杜克大学量子中心与物理系）；Department of Electrical and Computer Engineering, Duke University（杜克大学电气与计算机工程系）
We consider molecules confined to a microcavity whose dimensions are such that an excitation of the molecule is nearly resonant with a cavity mode. We investigate the situation where the excitation energies of the molecules are randomly distributed with a mean value of $ε_a$ and variance $σ$. For this case, we find a solution that approaches the exact result for large values of the number density $\mathscr{N}$ of the molecules. We find the conditions for the existence of the polaritonic states, as well as expressions for their energies. The polaritonic states are quite stable against disorder.…
We highlight the importance of quantum fluctuations in organizing a dissipative quantum phase transition for the driven Jaynes-Cummings interaction with variable qubit-cavity detuning. The system response presents a substantial difference from the predictions of the semiclassical theory, the extent of which is revealed in the properties of quantum bistability, and visualized with the help of quasi-distribution functions for the cavity field, subject to an appropriate scale parameter. States anticipated by the neoclassical theory of radiation coexist in the quantum picture, following the occurr…
Polaritons, mixed light-matter quasiparticles, undergo a transition to a condensed, macroscopically coherent state at low temperatures or high densities. Recent experiments show that coupling light to organic molecules inside a microcavity allows condensation at room temperature. The molecules act as saturable absorbers with transitions dressed by molecular vibrational modes. Motivated by this we calculate the phase diagram and spectrum of a modified Tavis-Cummings model, describing vibrationally dressed two-level systems, coupled to a cavity mode. Coupling to vibrational modes can induce re-e…
We study experimentally and theoretically a coherently-driven strongly-coupled quantum dot-microcavity system. Our focus is on physics of the unexplored intermediate excitation regime where the resonant laser field dresses a strongly-coupled single exciton-photon (polariton) system resulting in a ladder of laser-dressed Jaynes-Cummings states. In that case both the coupling of the emitter to the confined light field of the microcavity and to the light field of the external laser are equally important, as proved by observation of injection pulling of the polariton branches by an external laser.…
The exceptionally strong coupling realizable between superconducting qubits and photons stored in an on-chip microwave resonator allows for the detailed study of matter-light interactions in the realm of circuit quantum electrodynamics (QED). Here we investigate the resonant interaction between a single transmon-type multilevel artificial atom and weak thermal and coherent fields. We explore up to three photon dressed states of the coupled system in a linear response heterodyne transmission measurement. The results are in good quantitative agreement with a generalized Jaynes-Cummings model. Ou…
We explore how the Jaynes-Cummings ladder transpires in the emitted spectra of a two-level system in strong coupling with a single mode of light. We focus on the case of very strong coupling, that would be achieved with systems of exceedingly good quality (very long lifetimes for both the emitter and the cavity). We consider the incoherent regime of excitation, that is realized with semiconductors quantum dots in microcavities, and discuss how reasonable is the understanding of the systems in terms of transitions between dressed states of the Jaynes-Cummings Hamiltonian.
We consider a disordered quantum metamaterial formed by an array of superconducting flux qubits coupled to microwave photons in a cavity. We map the system on the Tavis-Cummings model accounting for the disorder in frequencies of the qubits. The complex transmittance is calculated with the parameters taken from state-of-the-art experiments. We demonstrate that photon phase shift measurements allow to distinguish individual resonances in the metamaterial with up to 100 qubits, in spite of the decoherence spectral width being remarkably larger than the effective coupling constant. Our simulation…
We follow the passage from complex amplitude bistability to phase bistability in the driven dissipative Jaynes-Cummings oscillator. Quasidistribution functions in the steady state are employed, for varying qubit-cavity detuning and drive parameters, in order to track a first-order dissipative quantum phase transition up to the critical point marking a second-order transition and spontaneous symmetry breaking. We demonstrate the photon blockade breakdown in the dispersive regime, and find that the coexistence of cavity states in the regime of quantum bistability is accompanied by pronounced qub…
We study the quantum dynamics of a single mode/particle interacting inhomogeneously with a large number of particles and introduce an effective approach to find the accessible Hilbert space where the dynamics takes place. Two relevant examples are given: the inhomogeneous Tavis-Cummings model (e.g., N atomic qubits coupled to a single cavity mode, or to a motional mode in trapped ions) and the inhomogeneous coupling of an electron spin to N nuclear spins in a quantum dot.
We investigate theoretically the many-emitter phonon laser based on optically driven semiconductor quantum dots within an acoustic nanocavity. We map the phonon laser Hamiltonian to a Tavis-Cummings type interaction with an unexpected additional many-emitter energy shift. This many-emitter interaction with the cavity mode results in a variety of resonances dependent on the number of participating emitters. We show that the many-emitter phonon laser also includes the single emitter resonance besides these collective phenomena. However, we obtain a high quantum yield addressing these collective …
Collective phenomena in the Tavis-Cummings model has been widely studied, focusing on the phase transition features. In many occasions, it has been used variational approaches that consider separated radiation-matters systems. In this paper, we examine the role of the quantum entanglement of an assembly of two-level emitters coupled to a single-mode cavity; this allows us to characterise the quantum correlated state for each regime. Statistical properties of the system, e.g., the first four statistical moments, show clearly the structure of the light and matter distributions. Even though the s…
We investigate theoretically how the spectroscopy of an ancillary qubit can probe cavity (circuit) QED ground states containing photons. We consider three classes of systems (Dicke, Tavis-Cummings and Hopfield-like models), where non-trivial vacua are the result of ultrastrong coupling between N two-level systems and a single-mode bosonic field. An ancillary qubit detuned with respect to the boson frequency is shown to reveal distinct spectral signatures depending on the type of vacua. In particular, the Lamb shift of the ancilla is sensitive to both ground state photon population and correlat…
We develop a new spectroscopic method to quickly and intuitively characterize the coupling of two microwave-photon-coupled semiconductor qubits via a high-impedance resonator. Highly distinctive and unique geometric patterns are revealed as we tune the qubit tunnel couplings relative to the frequency of the mediating photons. These patterns are in excellent agreement with a simulation using the Tavis-Cummings model, and allow us to readily identify different parameter regimes for both qubits in the detuning space. This method could potentially be an important component in the overall spectrosc…
