Probing the Dynamics of a Superradiant Quantum Phase Transition with a Single Trapped Ion

Abstract

We demonstrate that the quantum phase transition (QPT) of the Rabi model and critical dynamics near the QPT can be probed in the setup of a single trapped ion. We first show that there exists equilibrium and nonequilibrium universal functions of the Rabi model by finding a proper rescaling of the system parameters and observables. We then propose a scheme that can faithfully realize the Rabi model in the limit of a large ratio of the effective atomic transition frequency to the oscillator frequency using a single trapped-ion and therefore the QPT. It is demonstrated that the predicted universal functions can indeed be observed based on our scheme. Finally, the effects of realistic noise sources on probing the universal functions in experiments are examined.Introduction.-The experimental realization of quantum phase transition (QPT) in a well-controlled quantum system is of considerable interest [1][2][3][4][5][6][7][8][9]. This is particularly important for the study of the dynamics of QPT where a controlled change of the system parameters are necessary [10][11][12]. Understanding the dynamics of QPT is at the frontier of the study of critical phenomena; the full extent of the universality in non-equilibrium dynamics of a system that undergoes a QPT remains to be determined [13,14] and its theoretical underpinnings are being actively investigated [15][16][17][18][19][20].Trapped ions are a particularly promising platform for this purpose thanks to the possibility of precise coherent quantum controls and high-fidelity measurements [3][4][5] as exemplified by the recent observation of the dynamics of classical phase transitions [21,22]. A major challenge, however, lies in the fact that the QPT typically occurs in a thermodynamic limit where the number of system constituents diverges [23]. Although the universality manifests itself even for a system of finite size in the form of finite-size scaling relations [24,25], it emerges only when the system size is sufficiently large; moreover, a controlled change in the system size under otherwise unchanged conditions is necessary in order to observe the critical exponents. In this respect, and despite the advances in trapped-ion technologies, it is still a formidable challenge to scale up the system size sufficiently to enable the observation of critical phenomena while maintaining the controllability and the coherence of the system [5].Recently, it has been shown in Ref. [20,26] that even a single two-level atom coupled to a harmonic oscillator may undergo a second-order QPT. The experimental realization of such a finite-system QPT is highly desirable, as it opens a possibility to study the dynamics of QPT in a small, fully controlled quantum system with a high degree of coherence without the necessity of the scalability in the number of system components; however, the required parameter regime [20,26] that includes simultaneously extremely large detuning [27][28][29] and large coupling strength [30][31][32] has made it difficult to find a suitable experimental platform ...

Quantum Simulation of the Quantum Rabi Model in a Trapped Ion

“…From a theoretical point of view, our work justifies further research in light-matter coupling regimes that are a priori not found in nature, as we are providing a platform where all these regimes can be physically implemented. Our experimental methods can be directly extended to the study of the phase transition in the QRM [49][50][51] or to the simulation of the Dicke model [52][53][54] by considering the presence of more ions. configuration, we obtain the resonance frequency of the red-sideband transition with the detuning of the bluesideband transition fixed at δ b ¼ ð2πÞ625 kHz.…”

Connecting nth order generalised quantum Rabi models: Emergence of nonlinear spin-boson coupling via spin rotations

“…Even though the QRM has been exhaustively investigated in the last decades, a number of recent findings has brought it again into the research spotlight. Among them we can mention its integrability [13], the existence of a distinctive behaviour in the deep strong coupling regime [14], or the emergence of a quantum phase transition [15][16][17][18]. Closely related to the QRM, we find the nth order QRM (nQRM) which differs from the QRM in that the nQRM comprises n-boson exchange interaction terms because of the presence of a nonlinear spinboson coupling.…”

Open quantum systems with local and collective incoherent processes: Efficient numerical simulations using permutational invariance

“…IV F, it is possible to extract such an equation from the general dissipators we construct in PIQS. (Though this procedure is not strictly necessary in systems where the coupling is only "effectively" strong, and where the bare-basis master equation is still valid [28,29,78,[99][100][101][102][103][104][105][106][107]).…”