Dynamical Quantum Phase Transitions in the Dissipative Lipkin-Meshkov-Glick Model with Proposed Realization in Optical Cavity QED

Abstract

We present an optical cavity QED configuration that is described by a dissipative version of the Lipkin-Meshkov-Glick model of an infinitely coordinated spin system. This open quantum system exhibits both first-and second-order non-equilibrium quantum phase transitions as a single, effective field parameter is varied. Light emitted from the cavity offers measurable signatures of the critical behavior, including that of the spin-spin entanglement.PACS numbers: 42.50. Fx, 42.50.Pq, 03.65.Ud, 73.43.Nq Remarkable advances with trapped, ultra-cold atomic gases have opened up exciting new avenues of research into strongly interacting many-body quantum systems [1]. Exquisite control of both motional and electronic degrees of freedom of cold atoms can enable one to "tailor" atom-atom interactions and thereby implement a variety of systems that exhibit, in particular, quantum critical phenomena, i.e., transitions between distinct quantum phases, driven by quantum fluctuations, in response to variations of an effective field or interaction strength around some critical value.Recently, important insights into such transitions have been obtained from theoretical studies of the quantum entanglement properties of critical spin systems (see, e.g., [2,3,4,5,6,7,8,9,10]). Bipartite entanglement measures characterizing entanglement between a pair of spins (e.g., the concurrence) or between two blocks of spins (e.g., the entanglement entropy) can display marked critical behavior and scaling at quantum critical points. In this context, a simple but very useful example is the Lipkin-Meshkov-Glick (LMG) model [11], which is described by the Hamiltonianwhere {J x , J y , J z } are collective angular momentum operators for N spin-1/2 particles, h and λ are effective magnetic field and spin-spin interaction strengths, respectively, and γ ∈ [−1, 1] is an anisotropy parameter. This system, in which each spin interacts identically with every other spin, exhibits critical behavior at zero temperature; in particular, either first-or second-order equilibrium quantum phase transitions may occur, depending on the choice of λ and γ, as the ratio h/λ is varied across a critical value [6]. Notably, the second-order transition involves a change from a unique ground state (normal phase) to a pair of macroscopically displaced degenerate ground states (broken phase). Entanglement in the system displays the above-mentioned critical behavior, reaching, in particular, a pronounced maximum at the critical point [5,6,7].Given these interesting and topical features of the LMG model, it follows that the physical realization of a system described by such a model would provide a valuable test bed for studies of quantum critical phenomena and entanglement. Here we propose an open-system (i.e., dissipative) version of the LMG model based on the collective interaction of an ensemble of atoms with laser fields and field modes of a high-finesse optical resonator. In the spirit of a recent proposal for realizing the Dicke model [12], our scheme employs Raman tran...

Critical exponent of a quantum-noise-driven phase transition: The open-system Dicke model

“…Another collective spin model exhibiting dynamical QPT, the Lipkin-MeshkovGlick model was constructed in cavity QED systems [28]. We consider a single dissipation channel which is the photon leakage through one of the mirrors.…”

Finite-temperature quantum criticality in a complex-parameter plane

“…array of cavities [27,28], atoms within a cavity [29], and Rydberg atoms in an optical lattice [30][31][32][33]. Recently, it was pointed that [34], an imaginary transverse field may be implemented by optically pumping a qubit state into the auxiliary state.…”

Floquet engineering from long-range to short-range interactions

“…However, the nearest-neighbor interaction is small, and it is hard to cool the atoms to sufficiently low temperatures. This has motivated many experimental groups to create quantum simulators based on dipolar or Coulomb interactions [4][5][6][7][8][9]. The advantages of these setups are that the interaction strength is large and that the atoms do not have to be very cold.…”

“…The advantage of our approach is that it does not require individual addressing, since the magnetic-field gradient acts on all spins at the same time. Also, our approach is universal and can be applied to all experimental systems with long-range interactions: trapped ions [4], polar molecules [5,6], Rydberg atoms [7], nitrogen-vacancy (NV) centers [8], and cavity QED [9].…”

“…A common feature of such systems is the presence of long-range interactions that decay with a power law in distance due to dipolar or Coulomb interactions [4][5][6][7][8][9]. On the one hand, long-range interactions can lead to qualitatively new physics [10].…”