We predict large cooperative effect involving two atom two photon vacuum Rabi oscillations in a high quality cavity. The two photon emission occurs as a result of simultaneous de-excitation of both atoms with two photon resonance condition $ω_1+ω_2\approx ω_a+ω_b$, where $ω_1$, $ω_2$ are the atomic transition frequencies and $ω_a$, $ω_b$ are the frequencies of the emitted photons. The actual resonance condition depends on the vacuum Rabi couplings. The effect can be realized either with identical atoms in a bimodal cavity or with nonidentical atoms in a single mode cavity.
Within the framework of exact quantum electrodynamics in dispersing and absorbing media, we have studied the emission from an initially in the upper state prepared emitter in a high quality cavity in the case, when there are two cavity modes that resonantly interact with the emitter. In particular, when one of the modes is in resonance with the emitter transition and the other mode is tuned to the frequency equal to the Rabi splitting of the first mode, the effect of Rabi resonance is observed.
We study the coherent dynamics of an excited two-level atom in a vacuum optomechanical cavity and find that the original atom-cavity Rabi oscillation is sinusoidally modulated by the light-mechanics coupling as the Rabi splitting is on resonance with the mechanical mode. We develop an analytic model in a three-dimensional Hilbert subspace to explain this phenomenon and employ numerical simulations of the density-matrix master equation to confirm our analysis. We also show that the modulated Rabi oscillation survives in presence of dissipations and other non-ideal factors.
We propose a scheme of enhancement of Rabi coupling between two identical atomic ensembles trapped inside an optical cavity in a membrane-in-the-middle set up. The cavity modes dispersively interact with the ensembles and the effective interaction between the ensembles is governed by the tunnelling rate of the cavity modes through the oscillating membrane. We have shown that this interaction can be made large enough such that the Rabi oscillation occurs in a time-scale, much smaller than the relevant decay time-scales of the cavity modes and of the membrane. We present the detailed analytical …
Comparison of theory of Rabi oscillations with experiment [M. Wilczewski and M. Czachor, Phys. Rev. A {\bf 79}, 033836 (2009)] suggests that cavity lifetime parameters obtained in measurements with many photons may be much smaller than those applicable to almost vacuum states of light. In this context we show that the conclusion remains unchanged even if one takes a more realistic description of the initial state of light in cavity.
The dynamics of the Jaynes-Cummings Hamiltonian is studied in the semiclassical limit by reducing it to quantum normal form and deriving the phase space dynamics of classically smooth observables. The resulting systematic semiclassical approximation is used to analyze the Rabi oscillations of a photon wave packet revealing subtle consequences of the uncertainty principle.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED has been reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modif…
We investigate the Rabi oscillation of an atom placed inside a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. This proposal was studied previously with the use of Markov approximation, where the delay due to the finite travel time of light between the two cavity mirrors is neglected. We show that Rabi oscillation analogous to that obtained with high-finesse classical cavities is achieved only when this travel time is much larger than the time scale that characterizes the collective response of the atomic chain. Therefore, the delay must…
In this paper, we investigate the energy spectrum and coherent dynamical process in a cavity-QED setup with a moving emitter, which is subject to a harmonic potential. We find that the vibration of the emitter will induce the effective Kerr and optomechanical interactions. We generalize the Bogliubov operators approach which dealt with quantum Rabi model, to our cavity-emitter-vibration system and obtain the energy spectrum exactly. With the assistance of Bogliubov operators approach, we obtain the energy spectrum of the system exactly. Furthermore, we show that the dynamics of the system exhi…
In this letter, we investigate the dynamics of a single superconducting artificial atom capacitively coupled to a transmission line with a characteristic impedance comparable or larger than the quantum resistance. In this regime, microwaves are reflected from the atom also at frequencies far from the atom's transition frequency. Adding a single mirror in the transmission line then creates cavity modes between the atom and the mirror. Investigating the spontaneous emission from the atom, we then find Rabi oscillations, where the energy oscillates between the atom and one of the cavity modes.
We introduce the cross-cavity quantum Rabi model describing the interaction of a single two-level system with two orthogonal boson fields and propose its quantum simulation by two-dimensional, bichromatic, first-sideband driving of a single trapped ion. We provide an introductory survey of the model, including its diagonalization in the two-level system basis, numerical spectra and its characteristics in the weak, ultra strong and deep strong coupling regimes. We also show that the particular case of degenerate field frequencies and balanced couplings allows us to cast the model as two parity …
We discuss a cavity-QED scheme to deterministically generate entangled photons pairs by using a three-level atom successively coupled to two single longitudinal mode high-Q cavities presenting polarization degeneracy. The first cavity is prepared in a well defined Fock state with two photons with opposite circular polarizations while the second cavity remains in the vacuum state. A half-of-a-resonant Rabi oscillation in each cavity transfers one photon from the first to the second cavity, leaving the photons entangled in their polarization degree of freedom. The feasibility of this implementat…
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 spectr…
We study quantum optics with the atoms coupled to the quantized electromagnetic (EM) field in a non-inertial reference frame by making use of quantum field theory in curved spacetime. We rigorously establish the microscopic model for a two-level atom interacting with the quantized EM field in a rotating ring cavity by deriving a Jaynes-Cummings (JC) type Hamiltonian. Due to the two fold degeneracy of the ring cavity modes, the Rabi splitting exhibits three rather than two resonant frequency peaks. We find that the heights of the two side peaks show a sensitive linear dependence on the rotating…
The dynamics of a vibronic system in a lossy two-mode cavity is studied, with the first mode being resonant to the electronic transition and the second one being nearly resonant due to Raman transitions. We derive analytical solutions for the dynamics of this system. For a properly chosen detuning of the second mode from the exact Raman resonance, we obtain conditions that are closely related to the phenomenon of Rabi resonance as it is well known in laser physics. Such resonances can be observed in the spontaneous emission spectra, where the spectrum of the second mode in the case of weak Ram…
The transmission spectrum for one atom strongly coupled to the field of a high-finesse optical resonator is observed to exhibit a clearly resolved vacuum-Rabi splitting characteristic of the normal modes in the eigenvalue spectrum of the atom-cavity system. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements in cavity QED that have required averaging over many atoms.
We consider a generalized version of the Rabi model that includes a nonlinear, dispersive-type atom-field interaction in addition to the usual linear dipole coupling, as well as cavity dissipation. An effective system of this sort arises, for example, in a quantum simulation of the Rabi model based upon Raman transitions in an optical cavity QED setting [A. L. Grimsmo and S. Parkins, Phys. Rev. A {\bf87}, 033814 (2013)]. For a suitable choice of the nonlinear interaction strength, near degeneracies of the states in the cavity-mode vacuum and single-photon subspaces, in combination with cavity …
he effect of the counter-rotating terms in the Jaynes-Cummings model is investigated with an extended coherent-state approach. The counter-rotating terms greatly modify the vacuum Rabi splitting. Two peaks with different heights in the weak coupling regime and more than two peaks in the intermediate coupling regime are predicted. The collapses and revivals in the evolution of the atomic population inversion disappear in the intermediate coupling regime, but reappear in the strong coupling regime. This reappearance is similar to that under the rotating-wave approximation, attributed to the summ…
We present an interaction scheme that exhibits a dynamical consequence of virtual photons carried by a vacuum-field dressed two-level atom in the ultrastrong coupling regime. We show that, with the aid of an external driving field, virtual photons provide a transition matrix element that enables the atom to evolve coherently and reversibly to an auxiliary level accompanied by the emission of a real photon. The process corresponds to a type of vacuum Rabi oscillation, and we show that the effective vacuum Rabi frequency is proportional to the amplitude of a single virtual photon in the ground s…
The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasi-resonant with the cavity photon energy, and by neglecting the non resonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one is able to derive the well-known phenomenology of quasi-resonant transitions, includin…
The superradiant phase transition (SPT) controlled by the interacting strength between the two-level atom and the photons has been a hot topic in the Rabi model and the Rabi-dimer model. The latter describes two Rabi cavities coupled with an inter-cavity hopping parameter. Moreover, the SPT in the Rabi-dimer model is found to be the same universal class that in the Rabi model by investigating the correlation-length critical exponent. In this paper, we are concerned about whether the inter-cavity hopping parameter between two Rabi cavities (i.e., the Rabi-dimer model) will induce the SPT and to…
The Rabi Hamiltonian describes a single mode of electromagnetic radiation interacting with a two-level atom. Using the coupled cluster method, we investigate the time evolution of this system from an initially empty field mode and an unexcited atom. We give results for the atomic inversion and field occupation, and find that the virtual processes cause the field to be squeezed. No anti-bunching occurs.
Considering the intrinsic nonlinearity in a nanomechanical resonator coupled to a charge qubit, vacuum Rabi splitting effect is studied in a nanomechanical QED (qubit-resonator) system. A driven nonlinear Jaynes-Cummings model describes the dynamics of this qubit-resonator system. Using quantum regression theorem and master equation approach, we have calculated the two-time correlation spectrum analytically. In the weak driving limit, these analytical results clarify the influence of the driving strength and nonlinearity parameter on the correlation spectrum. Also, numerical calculations confi…
Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation and communication. Here we propose a method for the generation of very good approximations to highly squeezed vacuum states with low excess anti-squeezing using only a few oscillator-qubit coupling gates through a Rabi-type interaction Hamiltonian. This interaction can be implemented with several different methods, which has previously been demonstrated in superconducting circuit and trapped-ion platforms. The protocol is compatible with other protocols manipulating quantum harmo…
We have investigated vacuum Rabi oscillation of an atom coupled with single-mode cavity field exactly, and compared the results with that of J-C model. The results show that, there is damping Rabi oscillation for an atom, even in strong coupling regime. For small detuning and weak coupling case, the probability for the atom in excited state oscillates against time with different frequency and amplitude from that of J-C model. It exhibits the counter-rotating wave interaction could significantly effect the dynamic behavior of the atom, even under the condition in which the RWA is considered to …
We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) of the multimode quantum Rabi model(MQRM). We derive an analytic expression for the decay rate of the survival probability where cavity modes are initially prepared as thermal equilibrium states. A crossover from QZE to QAZE is observed due to the energy backflow induced by high frequency cavity modes. In addition, we apply a numerically exact method based on the thermofield dynamics(TFD) theory and the matrix product states(MPS) to study the effect of squeezing of the cavity modes on the QZE of the MQRM. The influence …
A coherent coupling among different energy photons provided by nonlinear optical interaction is regarded as a photonic version of the Rabi oscillation. Cavity enhancement of the nonlinearity reduces energy requirement significantly and pushes the scalability of the frequency-encoded photonic circuit based on the photonic Rabi oscillation. However, confinement of the photons in the cavity severely limits the number of interactable frequency modes. Here we demonstrate a wide-bandwidth and efficient photonic Rabi oscillation achieving full-cycle oscillation based on a cavity-enhanced nonlinear op…
We have numerically obtained theoretical results for the collapse and the revival of the quantum Rabi oscillations for low average number of coherent photons injected on a two-level system in a lossy resonant cavity. We have adopted the multimode Jaynes-Cummings model for the same and especially treated the ``Ohmic" loss to the walls of the cavity, the leakage from the cavity, and the loss due to the spontaneous emission through the open surface of the cavity. We have compared our results with the experimental data obtained by Brune et al [Phys. Rev. Lett. 76, 1800 (1996)] in this regard.
The paper continues the analysis of vacuum Rabi oscillations we started in Part I [Phys. Rev. A {\bf 79}, 033836 (2009)]. Here we concentrate on experimental consequences for cavity QED of two different classes of representations of harmonic oscillator Lie algebras. The zero-temperature master equation, derived in Part I for irreducible representations of the algebra, is reformulated in a reducible representation that models electromagnetic fields by a gas of harmonic oscillator wave packets. The representation is known to introduce automatic regularizations that in irreducible representations…
The quantum Rabi oscillations in a coherently driven quantum dot embedded in a high-Q doubly resonant semiconductor micro-cavity in the presence of a strong second-order nonlinear medium is investigated theoretically. It is shown that the second order nonlinearity effect the Rabi oscillations in a significant manner.
For two discrete-level quantum systems in interaction, we follow the displacement in the complex plane of the eigen-energies of the compound system when the spectrum of one of the two systems becomes continuous. These new points are usually called resonances. This allows us to define and to calculate a critical value of the coupling constant which separates two well-known coupling regimes. We also give an example of these resonances for the hydrogen atom coupled to the continuum of the states of the transverse electromagnetic field in the vacuum. We justify that some resonances be neglected.
We study the all-optical time-control of the strong coupling between a single cascade three-level quantum emitter and a microcavity. We find that only specific arrival-times of the control pulses succeed in switching-off the Rabi oscillations. Depending on the arrival times of control pulses, a variety of exotic non-adiabatic cavity quantum electrodynamics effects can be observed. We show that only control pulses with specific arrival times are able to suddenly switch-off and -on first-order coherence of cavity photons, without affecting their strong coupling population dynamics. Such behavior…
The 1996 Brune {\it et al.} experiment on vacuum Rabi oscillation is analyzed by means of alternative models of atom-reservoir interaction. Agreement with experimental Rabi oscillation data can be obtained if one defines jump operators in the dressed-state basis, and takes into account thermal fluctuations between dressed states belonging to the same manifold. Such low-frequency transitions could be ignored in a closed cavity, but the cavity employed in the experiment was open, which justifies our assumption. The cavity quality factor corresponding to the data is $Q=3.31\cdot 10^{10}$, whereas…
We study a special two-atom entanglement case in assumed Cavity QED experiment in which only one atom effectively exchanges a single photon with a cavity mode. We compute diatom entanglement under position-dependent atomic resonant dipole-dipole interaction (RDDI) for large interatomic separation limit. We show that the RDDI, even which is much smaller than the maximal atomic Rabi frequency, can induce distinct diatom entanglement. The peak entanglement (PE) reaches a maximum when RDDI strength can compare with the Rabi frequency of an atom.
We discuss the equilibrium and out of equilibrium dynamics of cavity QED in presence of dissipation beyond the standard perturbative treatment of losses. Using the dynamical polaron \emph{ansatz} and Matrix Product State simulations, we discuss the case where both light-matter $g$-coupling and system-bath interaction are in the ultrastrong coupling regime. We provide a critical $g$ for the onset of Rabi oscillations. Besides, we demonstrate that the qubit is \emph{dressed} by the cavity and dissipation. That such dressing governs the dynamics and, thus, it can be measured. Finally, we sketch a…
We report the observation of the vacuum Rabi splitting of a single quantum emitter by measuring its direct spontaneous emission into free space. We used a semiconductor quantum dot inside a photonic crystal nanocavity, in conjunction with an appropriate cavity design and filtering with a polarizer and an aperture, enabling the extraction of the inherently-weak emitter's signal. The emitter's vacuum Rabi spectra exhibit clear differences to those measured by detecting the cavity photon leakage. Moreover, we observed an asymmetric vacuum Rabi spectrum induced by interference between the emitter …
Two-photon Rabi splitting in a cavity-dot system provides a basis for multi-qubit coherent control in quantum photonic network. Here we report on two-photon Rabi splitting in a strongly coupled cavity-dot system. The quantum dot was grown intentionally large in size for large oscillation strength and small biexciton binding energy. Both exciton and biexciton transitions couple to a high quality factor photonic crystal cavity with large coupling strengths over 130 $μ$eV. Furthermore, the small binding energy enables the cavity to simultaneously couple with two exciton states. Thereby two-photon…
We examine cold atomic collisions within a resonant optical cavity. The quantized cavity mode can be used to manipulate the collisions between the cold atoms, such that periodic exchange of excitations between the atoms and the electromagnetic field strongly alters the collision dynamics. A colliding pair of atoms can thereby oscillate between its ground and excited states during the collision time. Using a semiclassical model, it can be predicted that such Rabi-like oscillations are revealed in the atomic trap-loss probabilities, which show maxima and minima as a function of the detuning betw…
We study a quantum dot strongly coupled to a single high-finesse optical microcavity mode. We use a rotating wave approximation method, commonly used in ion-laser interactions, tegether with the Lamb-Dicke approximation to obtain an analytic solution of this problem. The decay of Rabi oscillations because of the electron-phonon coupling are studied at arbitrary temperature and analytical expressions for the collapse and revival times are presented. Analyses without the rotating wave approximation are presented by means of investigating the energy spectrum.
We present an analytical solution of the single photon quantum feedback in a cavity quantum electrodynamics system based on a half cavity set-up coupled to a structured continuum. The exact analytical expression we obtain allows us to discuss in detail under which conditions a single emitter-cavity system, which is initially in the weak coupling regime, can be driven into the strong coupling regime via the proposed quantum feedback mechanism [Carmele et al, Phys.Rev.Lett. 110, 013601]. Our results reveal that the feedback induced oscillations rely on a well-defined relationship between the del…
Spin squeezing by geometric focusing in vacuum Rabi oscillations
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）；National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室、物理学院、现代工程与应用科学协同创新中心）；MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室与MIT-哈佛超冷原子中心）
When an atom strongly couples to a cavity, it can undergo coherent vacuum Rabi oscillations. Controlling these oscillatory dynamics quickly relative to the vacuum Rabi frequency enables remarkable capabilities such as Fock state generation and deterministic synthesis of quantum states of light, as demonstrated using microwave frequency devices. At optical frequencies, however, dynamical control of single-atom vacuum Rabi oscillations remains challenging. Here, we demonstrate coherent transfer of optical frequency excitation between a single quantum dot and a cavity by controlling vacuum Rabi o…
We report time-domain observation of vacuum Rabi oscillations in a single quantum dot strongly coupled to a nanocavity under incoherent optical carrier injection. We realize a photonic crystal nanocavity with a very high quality factor of >80,000 and employ it to clearly resolve the ultrafast vacuum Rabi oscillations by simple photoluminescence-based experiments. We found that the time-domain vacuum Rabi oscillations were largely modified when changing the pump wavelength and intensity, even when marginal changes were detected in the corresponding photoluminescence spectra. We analyze the meas…
The demonstration of enhanced spontaneous emission of nanoscaled optical emitters near metallic nanoparticles and the recent realization of a nanolaser based on surface plasmon amplification by stimulated emission of radiation (spaser) encourage the search for strong coupling regime at the nanoscale. Here we propose the concept of nanopolaritons. We demonstrate with accurate scattering calculations that the strong coupling regime of a single quantum emitter (a semiconductor quantum dot) placed in the gap between two metallic nanoparticles can be achieved. The largest dimension of the investiga…
The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of `cat' states, quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their qu…
We explore the long-time dynamics of Rabi model in a driven-dissipative setting and show that, as the atom-cavity coupling strength becomes larger than the cavity frequency, a new time scale emerges. This time scale, much larger than the natural relaxation time of the atom and the cavity, leads to long-lived metastable states susceptible to being observed experimentally. By applying a Floquet-Liouville approach to the time-dependent master equation, we systematically investigate the set of possible metastable states. We find that the properties of the metastable states can differ drastically f…
We investigate the spectrum of energy and eigenstates of a hybrid cavity optomechanical system, where a cavity field mode interacts with a mechanical mode of a vibrating end mirror via radiation pressure and with a two level atom via electric dipole interaction. In the spirit of approximations developed for the quantum Rabi model beyond rotating-wave approximation (RWA), we implement the so-called generalized RWA (GRWA) to diagonalize the tripartite Hamiltonian for arbitrary large couplings. Notably, the GRWA approach still allows to rewrite the hybrid Hamiltonian in a bipartite form, like a R…
Toida et al. claim in their recent article [Phys. Rev. Lett. 110, 066802 (2013)] that they `report a direct observation of vacuum Rabi splitting in a GaAs/AlGaAs double quantum dot (DQD) based charge qubit coupled with a superconducting coplanar waveguide (CPW) resonator'. In this comment, we challenge the main claims made in their paper and show that their results: a) do not provide any evidence of vacuum Rabi oscillations and b) do not provide any direct evidence of vacuum Rabi splitting.
We consider the feedback stabilization of Rabi oscillations in a superconducting qubit which is coupled to a microwave readout cavity. The signal is readout by homodyne detection of the in-phase quadrature amplitude of the weak measurement output. By multiplying the time-delayed Rabi reference, one can extract the signal, with maximum signal-to-noise ratio, from the noise. We further track and stabilize the Rabi oscillations by using Lyapunov feedback control to properly adjust the input Rabi drives. Theoretical and simulation results illustrate the effectiveness of the proposed control law.
