Bimodal phase transition in a periodically modulated $\Lambda$-type three-level system

TL;DR

This paper theoretically explores how periodic modulation in a three-level quantum system can induce bimodal phase transitions, revealing new ways to control quantum phases within an extended Jaynes-Cummings framework.

Contribution

It introduces a method to induce and analyze bimodal quantum phase transitions in a driven three-level system using an effective Hamiltonian approach.

Findings

Bimodal superradiant phases can be achieved by tuning modulation parameters.

The effective Hamiltonian accurately describes the driven system within certain approximations.

Dynamical quantum phase transitions are controllable via external periodic modulation.

Abstract

We present a theoretical investigation of dynamical quantum phase transitions (QPTs) in a periodically driven $\Lambda$-type three-level system (3LS) embedded in a double-mode cavity, described by a three-level Jaynes-Cumming (3L-JC) Hamiltonian. To begin with, we probe the undriven static Hamiltonian in the dressed-state basis to identify and define distinct coupling regimes and critical points associated with both cavity modes. Furthermore, to investigate the dynamical QPTs in this system, we incorporate a periodic modulation across two atomic states (denoted by $|3\rangle_{at}$ and $|2\rangle_{at}$) out of the three available energy levels. By performing necessary transformations and approximations, we reduce the overall Hamiltonian, which contains static and dynamic modulation terms, into an effective 3L-JC Hamiltonian whose system parameters are dependent on the driving parameters. The validity of our approximations is verified using the Loschmidt echo of time-evolved states corresponding to Hamiltonians before and after the approximations. Finally, we demonstrate that by tuning the modulation parameters, it is possible to explore bimodal superradiant phases in a three-level $\Lambda$-type system while remaining within the critical coupling limits of the static Hamiltonian. Our results provide an insight into the manipulation of quantum phases in a three-level system within an effective extended Jaynes-Cummings regime.