Simulating Anisotropic quantum Rabi model via frequency modulation

Abstract

Anisotropic quantum Rabi model is a generalization of quantum Rabi model, which allows its rotating and counter-rotating terms to have two different coupling constants. It provides us with a fundamental model to understand various physical features concerning quantum optics, solid-state physics, and mesoscopic physics. In this paper, we propose an experimental feasible scheme to implement anisotropic quantum Rabi model in a circuit quantum electrodynamics system via periodic frequency modulation. An effective Hamiltonian describing the tunable anisotropic quantum Rabi model can be derived from a qubit-resonator coupling system modulated by two periodic driving fields. All effective parameters of the simulated system can be adjusted by tuning the initial phases, the frequencies and the amplitudes of the driving fields. We show that the periodic driving is able to drive a coupled system in dispersive regime to ultrastrong coupling regime, and even deep-strong coupling regime. The derived effective Hamiltonian allows us to obtain pure rotating term and counter-rotating term. Numerical simulation shows that such effective Hamiltonian is valid in ultrastrong coupling regime, and stronger coupling regime. Moreover, our scheme can be generalized to the multi-qubit case. We also give some applications of the simulated system to the Schrödinger cat states and quantum gate generalization. The presented proposal will pave a way to further study the stronger anisotropic Rabi model whose coupling strength is far away from ultrastrong coupling and deep-strong coupling regimes in quantum optics.

Attempt to find the hidden symmetry in the asymmetric quantum Rabi model

“…An interesting physical model in relation to symmetry is the asymmetric quantum Rabi model (QRM) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], which we shall describe in more detail below. This model does not seem to possess any symmetry.…”

Effective and Efficient Resonant Transitions in Periodically Modulated Quantum Systems

“…Effective transitions in time-dependent quantum systems have been extensively studied since the classical paper [1], later generalized in [2], [3] and widely applied for the description of atomic dynamics in external fields [4][5][6][7][8][9][10][11][12][13][14][15][16] and in more involved periodically perturbed quantum systems [17][18][19][20][21][22][23]. Effective transitions are described by operators that: (i) Become time-independent (resonant) in an appropriate reference frame under certain relations between the system's frequencies (resonant conditions); (ii) are not present in the original Hamiltonian; and (iii) disappear in the rotating wave approximation (RWA).…”

“…In these types of models, CR terms (in the absence of external fields) are responsible for several physical effects such as: Multiphoton atom-field interactions in the Rabi model [25,26], an improvement of a qubit photodetector readout [27], the excitation of several atoms by a single photon [25,28], and several other effective processes now experimentally achievable in solid state circuit quantum electrodynamics (QED) setups [29][30][31][32]. An additional periodic excitation makes the situation even richer, leading to e.g., the enhancement of CR interactions in the Rabi model [16], the generation of specific non-classical photon states [17], the emergence of non-linear spin-boson couplings [18], the appearance of quantum to classical phase-transitions [19], lasing with a single atom [20], simulation of the anisotropic Rabi model [21], or the dynamical Casimir effect [22].…”

“…An additional periodic excitation makes the situation even richer, leading to e.g., the enhancement of CR interactions in the Rabi model [14], the generation of specific non-classical photon states [15], the emergence of non-linear spin-boson couplings [16], the appearance of quantum to classical phase-transitions [17], lasing with a single atom [18], simulation of the anisotropic Rabi model [19], or the dynamical Casimir effect [20].…”

Universal fluctuations and squeezing in generalized Dicke model near the superradiant phase transition

“…In the present work we are focused on another example of generalization, the anisotropic qubit-cavity interaction, i.e., when strengths of rotating-and counterrotating wave terms are different. The possible examples of systems, where such coupling can be realized, are frequency-modulated [22] or inductively and capacitively coupled [23] superconducting qubits, semiconductor heterostructures with spin-orbital interaction [24] and atoms in crossed electric and magnetic fields, see Ref. [25] for a review and also references therein.…”