We demonstrate the emergence of selective $k$-photon interactions in the strong and ultrastrong coupling regimes of the quantum Rabi model with a Stark coupling term. In particular, we show that the interplay between the rotating and counter-rotating terms produces multi-photon interactions whose resonance frequencies depend, due to the Stark term, on the state of the bosonic mode. We develop an analytical framework to explain these $k$-photon interactions by using time-dependent perturbation theory. Finally, we propose a method to achieve the quantum simulation of the quantum Rabi model with a Stark term by using the internal and vibrational degrees of freedom of a trapped ion, and demonstrate its performance with numerical simulations considering realistic physical parameters.
Optically-driven Rabi oscillations of single electron spins in a diamond nitrogen vacancy center are realized with two Raman-resonant optical pulses that are detuned from the respective dipole optical transitions. The Rabi oscillations are nuclear-spin selective and are robust against rapid decoherence of the underlying optical transitions, opening the door to generating phonon-mediated spin entanglement in an optically-driven spin-phonon system. A direct comparison between the Rabi oscillations and simulated Raman adiabatic passage along with a detailed theoretical analysis provide a wealth o…
State selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules or quantum dots is a the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for…
In the previous paper on this topic it was shown how, for a pulse of arbitrary shape and duration, the drive frequency can be analytically optimized to maximize the amplitude of the population oscillations between the selected two levels in a general many level quantum system. It was shown how the standard Rabi theory can be extended beyond the simple two-level systems. Now, in order to achieve the quickest and as complete as possible population transfer between two pre-selected levels, driving pulse should be tailored so that it produces only a single half-oscillation of the population. In th…
The asymmetric quantum Rabi model (AQRM) has a broken $\mathbb{Z}_2$ symmetry, with generally a non-degenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the $\mathbb{Z}_2$-symmetric quantum Rabi model are recovered, however, without any obvious parity-like symmetry. This unknown "symmetry" has thus been referred to as hidden symmetry in the literature. Here we show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asy…
Hybrid interactions between light and two-level systems and their nonlinear nature are crucial components of advanced quantum information processing and quantum networks. Rabi interaction exhibits the hybrid nonlinear nature, but its implementation is challenging at optical frequencies where the rotating wave approximation (RWA) is valid. Here, we propose a setup to conditionally induce Rabi interaction between discrete variable and continuous variable of traveling beams of light. We show that our scheme can generate Rabi interaction on weak states of light, where signatures of the nonlinear q…
We demonstrate Rabi flopping of small numbers of $\rm{^{87}Rb}$ atoms between ground and Rydberg states with $n\le 43$. Coherent population oscillations are observed for single atom flopping, while the presence of two or more atoms decoheres the oscillations. We show that these observations are consistent with van der Waals interactions of Rydberg atoms.
We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46, 265302 (2013)], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated.
For a system composed of nine qubits, we show that natural interactions among the qubits induce the time evolution that can be regarded, at discrete times, as the Rabi oscillation of a logical qubit. Neither fine tuning of the parameters nor switching of the interactions is necessary. Although straightforward application of quantum error correction fails, we propose a protocol by which the logical Rabi oscillation is protected against all single-qubit errors. The present method thus opens a simple and realistic way of protecting the unitary time evolution against noise.
We propose a method to create selective interactions with Dicke-Stark model by means of time-dependent perturbation theory. By choosing the proper rotating framework, we find that the time oscillating terms depend on the number of atomic excitations and the number of photonic excitations. Consequently, the Rabi oscillation between selective states can be realized by properly choosing the frequency of the two-level system. The second order selective interactions can also be studied with this method. Then various states such as Dicke states, superposition of Dicke states and GHZ states can be cr…
We present a fast quantum entangling operation on superconducting qubits assisted by a resonator in the quasi-dispersive regime with a new effect --- the selective resonance coming from the amplified qubit-state-dependent resonator transition frequency and the tunable period relation between a wanted quantum Rabi oscillation and an unwanted one. This operation does not require any kind of drive fields and the interaction between qubits. More interesting, the non-computational third excitation states of the charge qubits can play an important role in shortening largely the operation time of the…
We present an interaction scheme to control counter-rotating terms in the quantum Rabi model. We show that by applying a sequence of $π/2$ phase kicks to a two-level atom and a single mode quantized field, the natural dynamics of the Rabi model can be interrupted in a way that counter-rotating transitions can be significantly enhanced. This is achieved by a suitable timing of the phase kicks determined by a phase matching condition. If the time between successive kicks is sufficiently short, our scheme is turned into a dynamical decoupling problem in which the effects of counter-rotating terms…
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…
This paper provides a scheme for generating maximally entangled qubit states in the anti-Jaynes-Cummings interaction mechanism, so called entangled anti-polariton qubit states. We demonstrate that in an initial vacuum-field, Rabi oscillations in a cavity mode in the anti-Jaynes-Cummings interaction process, occur in the reverse sense relative to the Jaynes-Cummings interaction process and that time evolution of entanglement in the anti-Jaynes-Cummings interaction process takes the same form as in the Jaynes-Cummings interaction process. With the generated anti-polariton qubit state as one of t…
By exact numerical and master equation approaches, we show that a central spin-1/2 can be configured to probe internal bath dynamics. System-bath interactions cause Rabi oscillations in the detector and periodic behavior of fidelity. This period is highly sensitive to the strength of the bath self-interactions, and can be used to calculate the intra-bath coupling.
We study the ground states of the single- and two-qubit asymmetric Rabi models, in which the qubit-oscillator coupling strengths for the counterrotating-wave and corotating-wave interactions are unequal. We take the transformation method to obtain the approximately analytical ground states for both models and numerically verify its validity for a wide range of parameters under the near-resonance condition. We find that the ground-state energy in either the single- or two-qubit asymmetric Rabi model has an approximately quadratic dependence on the coupling strengths stemming from different cont…
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…
We propose a practical approach to manipulate the counter-rotating (CR) interactions in the quantum Rabi model by introducing a sinusoidal modulation to the transition frequency of the quantum two-level system in this model. By choosing appropriate modulation frequency and amplitude, enhancement and suppression of the CR interactions can be achieved in the Jaynes-Cummings regime (including both weak- and strong-coupling cases) as well as the ultrastrong-coupling regime. In particular, we calculate the output photon emission of the cavity vacuum state under enhanced CR terms. Our results show t…
We theoretically study the superradiant phase transition (SPT) in an indirect Rabi model, where both a two-level system and a single mode bosonic field couple to an auxiliary bosonic field. We find that the indirect spin-field coupling induced by the virtual excitation of the auxiliary field can allow the occurrence of a SPT at a critical point, and the influence of the so-called $A^2$ term in the normal Rabi model is naturally avoided. In the large detuning regime, we present the analytical expression of quantum critical point in terms of the original system parameters. The critical atom-fiel…
We propose a scheme to simulate the interaction between a two-level system and a classical light field. Under the transversal driving of two microwave tones, the system Hamiltonian is identical to that of the general semi-classical Rabi model. We experimentally realize this Hamiltonian with a superconducting transmon qubit. By tuning the strength, phase and frequency of the two microwave driving fields, we simulate the quantum dynamics from weak to extremely strong driving regime. The resulting evolutions gradually deviate from the normal sinusoidal Rabi oscillations with increasing driving st…
Quantum Rabi model (QRM) is fascinating not only because of its broad relevance and but also due to its few-body quantum phase transition. In practice both the bias and the nonlinear coupling in QRM are important controlling parameters in experimental setups. We study the interplay of the bias and the nonlinear interaction with the linear coupling in the ground state which exhibits various patterns of symmetry breaking and different orders of transitions. Several situations of tricriticality are unveiled in the low frequency limit and at finite frequencies. We find that the full quantum-mechan…
The two-photon Rabi Hamiltonian is a simple model describing the interaction of light with matter, with the interaction being mediated by the exchange of two photons. Although this model is exactly soluble in the rotating-wave approximation, we work with the full Hamiltonian, maintaining the non-integrability of the model. We demonstrate that, despite this non-integrability, there exist isolated, exact solutions for this model analogous to the so-called Juddian solutions found for the single-photon Rabi Hamiltonian. In so doing we use a Bogoliubov transformation of the field mode, as described…
This article is a response to the continued assumption, cited even in reports and reviews of recent experimental breakthroughs and advances in theoretical methods, that the antiJaynes-Cummings (AJC) interaction is an intractable energy non-conserving component of the quantum Rabi model (QRM). We present three key features of QRM dynamics : (a) the AJC interaction component has a conserved excitation number operator and is exactly solvable (b) QRM dynamical space consists of a rotating frame (RF) dominated by an exactly solved Jaynes-Cummings (JC) interaction specified by a conserved JC excitat…
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…
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 …
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…
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 …
Atomic spectroscopy, an essential tool for frequency estimation, is widely used in quantum sensing. Atom-atom interaction can be used to generate entanglement for achieving quantum enhanced sensing. However, atom-atom interaction always induces collision shift, which brings systematic error in determining the resonance frequency. Contradiction between utilizing atom-atom interaction and suppressing collision shift generally exists in atomic spectroscopy. Here, we propose an antisymmetric Rabi spectroscopy protocol without collision shift in the presence of atom-atom interactions. We analytical…
We give a mathematical procedure to obtain the adiabatic approximation for the generalized quantum Rabi Hamiltonian both without and with a quadratic interaction. We consider the Hamiltonian as the energy of a model describing the interaction system of a two-level artificial atom and a one-mode microwave photon in circuit QED. In the case without the quadratic interaction, we show in the adiabatic approximation that whether each bare eigenstate forms a Schrodinger-cat-like entangled state or not depends on whether the energy bias of the atom is zero or non-zero, and then, the effect of the tun…
We propose a superconducting circuit to implement a two-photon quantum Rabi model in a solid-state device, where a qubit and a resonator are coupled by a two-photon interaction. We analyze the input-output relations for this circuit in the strong coupling regime and find that fundamental quantum optical phenomena are qualitatively modified. For instance, two-photon interactions are shown to yield single- or two-photon blockade when a pumping field is either applied to the cavity mode or to the qubit, respectively. In addition, we derive an effective Hamiltonian for perturbative ultrastrong two…
Diffraction of light sets the fundamental limit for optical lithography. Many quantum lithography schemes have so far been proposed to overcome this limit either by making use of highly entangled photons, multi-photon processes or multiple Lambda transitions, which are all experimentally high-demanding. Recently, Liao et al. proposed a novel quantum lithography scheme which merely employs Rabi oscillation to surpass the diffraction limit. Here we report a faithful experimental realization of this scheme. Resolution up to ninth of the Rayleigh diffraction limit has been observed. Possibility of…
We show that the Casimir-Polder interaction may induce coherent oscillations between degenerate atomic states. We illustrate this effect by computing the Casimir-Polder induced Rabi frequency on a $^{87}$Rb atom as it interacts with a reflecting surface. The atom oscillates between two Zeeman sublevels of its ground state undergoing a periodic exchange of angular momentum with the vacuum photons.
The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonlizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By…
From the high vibrational dipolar strength offered by molecular liquids, we demonstrate that a molecular vibration can be ultra-strongly coupled to multiple IR cavity modes, with Rabi splittings reaching $24\%$ of the vibration frequencies. As a proof of the ultra-strong coupling regime, our experimental data unambiguously reveal the contributions to the polaritonic dynamics coming from the anti-resonant terms in the interaction energy and from the dipolar self-energy of the molecular vibrations themselves. In particular, we measure the opening of a genuine vibrational polaritonic bandgap of c…
A quantum memory protocol of controlled ac Stark echoes (CASE) based on a double rephasing photon echo scheme via controlled Rabi flopping is proposed. A double rephasing scheme of photon echoes inherently satisfies the no-population inversion requirement for quantum memories, but the resultant absorptive echo has been a fundamental problem. In the present studies, firstly, the first echo in the double rephasing scheme is dynamically controlled not to affect the second echo by using unbalanced ac Stark shifts. Secondly, a control Rabi pulse coherently manipulates the second echo to be emissive…
We considered one-dimensional chain of the two-level quantum systems coupled via tunneling. The chain is driven by the superposition of dc and ac fields in the strong coupling regime. Based on the fundamental principles of electrodynamics and quantum theory, we developed a generalized model of quantum dynamics for such interactions, free of rotating wave approximation (RWA). The system of motion equations was studied numerically. We analyzed the dynamics and spectra of inversion density, dipole current density and tunneling current density. In the case of resonant interaction with ac-component…
We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a sideband cooling blockade, stopping the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We compare the linear and nonlinear cases of these models in the ultrastrong and deep strong coupling regimes. Moreover, we propose a scheme that simulates the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red and blue sideband interactions, yielding applications as a dynamical qua…
In a hybrid optomechanical setup consisting of a two-level atom in a cavity with a pendular end-mirror, the interplay between the light field's radiation pressure on the mirror and the dipole interaction with the atom can lead to a blockade effect, which manifests itself in a suppression of Rabi oscillations in the atomic population. This effect is present when the system is in the single photon strong coupling regime and has an analogy in the photon blockade of optomechanics.
The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation (RWA). The RWA breaks down in the ultra-strong coupling (USC) regime, where the effective coupling strength $g$ is comparable to the energy $ω$ of the bosonic mode, and remarkable features in the system dynamics are revealed. We demonstrate an analog quantum simulation of an effec…
We investigate the applicability of the two major approximations which are most commonly employed in the study of the quantum Rabi model, namely the description of a resonant cavity mode as a single-mode quantized field and the use of the rotating wave approximation. Starting from the Hamiltonian of a two-level system interacting with a multi-mode quantized field, we perform the canonical transformation of the field operators. This allows one to partition the Hamiltonian of the system into two parts. The first part is the interaction of the two-level system with a single collective field mode,…
The Rabi model describes the simplest interaction between light and matter via a two-level quantum system interacting with a bosonic field. We demonstrate that the fully quantised version of the Rabi model is integrable in the Yang-Baxter sense at two parameter values. The model is argued to be not Yang-Baxter integrable in general. This is in contrast to the claim that the quantum Rabi model is integrable based on a phenomenological criterion of quantum integrability not presupposing the existence of a set of commuting operators. Similar Yang-Baxter integrable points are identified for the ge…
We show that it is possible to realize quantum superpositions of switched-on and -off strong light-matter interaction in a single quantum dot- semiconductor microcavity system. Such superpositions enable the observation of counterintuitive quantum conditional dynamics effects. Situations are possible where cavity photons as well as the emitter luminescence display exponential decay but their joint detection probability exhibits vacuum Rabi oscillations. Remarkably, these quantum correlations are also present in the nonequilibrium steady state spectra of such coherently driven dissipative quant…
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 …
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 establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts where spin-boson interactions are nonlinear as they comprise a simultaneous exchange of $n$ bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e. nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an…
We have analyzed the interaction of a dissipative two level quantum system with high and low frequency excitation. The system is continuously and simultaneously irradiated by these two waves. If the frequency of the first signal is close to the level separation and the second one is tuned to the Rabi frequency, it is shown that the response of the system exhibits an undamped low frequency oscillation. The method can be useful for low frequency Rabi spectroscopy in various physical systems which are described by a two level Hamiltonian, such as nuclei spins in NMR, double well quantum dots, sup…
The quantum Rabi model (QRM) describes the interaction between a two-level system (qubit) and a quantum harmonic oscillator. In the limit where the qubit frequency is smaller than the harmonic frequency, the QRM can be well approximated by the adiabatic approximation (AA). The AA is widely used due to its simplicity and explicit physical interpretation. However, the level crossings in the spectrum of the QRM predicted by the AA are determined by the zeros of Laguerre polynomials, which deviate from the exact points. We propose a new approximation to the QRM that predicts the level crossings co…
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…
QED-model for the multichain qubit system with interactions of qubits and chains between themselves on the example of the system of $σ$-polarons in carbon zigzag nanotubes, interacting with quantized EM-field, is considered analytically. The possibility of experimental detection of Rabi waves in conventional stationary optical experiments for any quasi-1D system with strong electron-photon interaction is predicted.
We map a quantum Rabi ring, consisting of $N$ cavities arranged in a ring geometry, into an effective magnetic model containing the XY exchange and the Dzyaloshinskii Moriya (DM) interactions. The analogue of the latter is induced by an artificial magnetic field, which modulates photon hopping between nearest-neighbor cavities with a phase. The mean-field behavior of both systems is almost identical, facilitating the description of the different phases in the quantum optical model through simple arguments of competing magnetic interactions. For the square geometry ($N=4$) the rich phase diagra…
The interacting model describing the Rabi transition is essential in studying atom-photon interactions, where the kinetic energy term is often neglected for the convenience of analysis. We first study the approximation through the fidelity approach and verify its valid region in the parameter space of detuning and momentum. We find that as the radiation field's momentum and the absolute value of detuning decrease, the approximation becomes valid. We further discover that the omission of the kinetic energy term will overestimate the measuring accuracy of the Rabi frequency in some parameter reg…
With a resonant amplitude-modulation field on two Rydberg atoms, we propose a Rydberg antiblockade (RAB) regime, where the Rabi oscillation between collective ground and excited states is induced. A controlled-Z gate can be yielded through a Rabi cycle. Further, several common issues of the RAB gates are solved by modifying the parameter relation. The gate fidelity and the gate robustness against the control error are enhanced with a shaped pulse. The requirement of control precision of the Rydberg-Rydberg interaction strength is relaxed. In addition, the atomic excitation is restrained and th…
