By applying the Bogoliubov transformations and through the introduction of the Bargmann-Hilbert spaces, we obtain analytic representations of solutions to the driven Rabi model without ${\cal Z}_2$ symmetry, and the 2-photon and two-mode quantum Rabi models. In each case, transcendental function is analytically derived whose zeros give the energy spectrum of the model. The zeros can be numerically found by standard root-search techniques.
The analytically exact solutions to the two-photon Rabi-Stark model are given by using the Bogoliubov operators approach. Transcendental functions responsible for the exact solutions are derived. The zeros of the transcendental functions reproduce completely the regular spectra. The first-order quantum phase transitions are also detected by the pole structure of the derived transcendental functions, similar to the one-photon Rabi-Stark model, different from the two-photon Rabi model where the energy levels for the ground-state and the first excited state do not cross. The spectra collapse char…
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 investigate the quantum phase transition in the dissipative anisotropic quantum Rabi model in the framework of quantum dressed master equation. From perspectives of both numerical and analytical analysis, we unravel the implication of the giant photon-bunching feature on the first-order quantum phase transition. The observed two-photon statistics can be well described analytically within a few lowest eigenstates at the low temperature. Moreover, such significant photon-bunching peak is generally exhibited at the deep-strong qubit-photon coupling, which is however lacking in the dissipative …
General solutions to the quantum Rabi model involve subspaces with unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for arbitrary number of qubits and photon modes. Unlike the Juddian solution, ours exists for arbitrary single qubit-photon coupling strength with constant eigenenergy. This corresponds to a horizontal line in the spectrum, while still being a qubit-photon entangled state. As a possible application, we propose an adiabatic scheme for the fast generation of arbitrary single-photon multimode W states with non…
Quantum emitters with a $Λ$-type level structure enable numerous protocols and applications in quantum science and technology. Understanding and controlling their dynamics is, therefore, one of the central research topics in quantum optics. Here, we drive two-photon Rabi oscillations between the two ground states of cesium atoms and observe the associated oscillatory Raman gain and absorption that stems from the atom-mediated coherent photon exchange between the two drive fields. The atoms are efficiently and homogeneously coupled with the probe field by means of a nanofiber-based optical inte…
The collective dynamics of two non-interacting two-level emitters, which are coupled to a structured wave guide that supports two-photon bound states, is investigated. Tuning the energy of the two emitters such that they are in resonance with the two-photon bound state energy band, we identify parameter regimes where the system displays fractional populations and essentially undamped Rabi oscillations. The Rabi oscillations, which have no analog in the single-emitter dynamics, are attributed to the existence of a collective polaron-like photonic state that is induced by the emitter-photon coup…
The true level crossings in a subspace of the asymmetric two-photon quantum Rabi model (tpQRM) have been observed when the bias parameter of qubit is an even multiple of the renormalized cavity frequency. Generally, such level crossings imply the existence of the hidden symmetry because the bias term breaks the obvious symmetry exactly. In this work, we propose a Bogoliubov operator approach (BOA) for the asymmetric tpQRM to derive the symmetry operators associated with the hidden symmetry hierarchically. The explicit symmetry operators consisting of Lie algebra at low biases can be easily obt…
Controllable interaction between photons and distant spins via vacuum Rabi oscillations
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子纳米科学卡弗里研究所）；Netherlands Organization for Applied Scientific Research (TNO)（荷兰应用科学研究组织）
Engineering Photon Delocalization in a Rabi Dimer with a Dissipative Bath
利用Rabi二聚体模拟了一个最近报道的由两个耦合传输线谐振器组成的电路量子电动力学系统，每个谐振器耦合到一个量子比特。在这项研究中，采用声子浴来模拟多模微机械谐振器，并耦合到拉比二聚体中的量子比特。利用Dirac-Frenkel含时变分原理结合Davydov D $_{2}$方法研究了该复合系统的动力学行为.最初，所有的光子都被泵入左谐振腔，两个量子比特处于与声子真空耦合的向下状态。在强量子位-光子耦合机制中，可以通过调节量子位-浴耦合强度$α$来设计光子动力学，并且通过增加$α$来实现光子离域。在没有耗散的情况下，光子局限于初始谐振腔中。然而，在适度的量子位浴耦合的情况下，光子在两个谐振器中长时间地随着光子布居的准平衡而离域。在这种情况下，高频浴模式通过与去极化量子位相互作用来激活。对于强耗散，光子离域是通过两个谐振器内的频繁光子跳跃来实现的，并且量子比特被抑制在它们的初始向下状态。
We study the ground state phase diagram of a nonlinear two-photon Rabi-Hubbard (RH) model in one dimension using quantum Monte Carlo (QMC) simulations and density matrix renormalization group (DMRG) calculations. Our model includes a nonlinear photon-photon interaction term. Absent this term, the RH model has only one phase, the normal disordered phase, and suffers from spectral collapse at larger values of the photon-qubit interaction or inter-cavity photon hopping. The photon-photon interaction, no matter how small, stabilizes the system which now exhibits {\it two} quantum phase transitions…
The Rabi model describes the simplest nontrivial interaction between a few-level system and a bosonic mode, featuring in multiple seemingly unrelated systems of importance to quantum science and technology. While exact expressions for the energies of this model and its few-mode extensions have been obtained, they involve roots of transcendental functions and are thus cumbersome and unintuitive. Utilizing the symmetric generalized rotating wave approximation (S-GRWA), we develop a family of approximations to the energies of the two-mode two-photon Rabi model. The simplest elements of the family…
The generalized Rabi model (gRM) with both one- and two-photon coupling terms has been successfully implemented in circuit quantum electrodynamics systems. In this paper, we examine theoretically multiphoton resonances in the gRM and derive their effective Hamiltonians. With different detunings in the system, we show that all three- to six-photon resonances can be achieved by involving two intermediate states. Furthermore, we study the interplay between multiphoton resonance and chiral transport of photon Fock states in a resonator junction with broken time-reversal symmetry. Depending on the …
This paper presents a proof of the existence of novel bound states of the two-photon quantum Rabi model at the collapse point. The two-photon Rabi model is interesting not only for its important role on non-linear light-matter interaction, but also for the exhibition of many-energy-levels degenerating process called the "spectral collapse". The squeezing property of the two-photon annihilation and creation operators is the origin for this phenomenon which is well studied without the energy-slitting term $ω_0$. However, many numerical studies have pointed out that with the presence of $ω_0$ , s…
In this paper, we uncover the elusive level crossings in a subspace of the asymmetric two-photon quantum Rabi model (tpQRM) when the bias parameter of qubit is an even multiple of the renormalized cavity frequency. Due to the absence of any explicit symmetry in the subspace, this double degeneracy implies the existence of the hidden symmetry. The non-degenerate exceptional points are also given completely. It is found that the number of the doubly degenerate crossing points in the asymmetric tpQRM is comparable to that in asymmetric one-photon QRM in terms of the same order of the constrained …
