Entanglement and bifurcations in Jahn-Teller models

Abstract

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The E ␤ system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the E models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the E ␤ system, the ground states of the E model always exhibit entanglement. For the E ␤ case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the E case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.

Jahn-Teller instability in dissipative quantum systems

“…The rate of change of entanglement as a function of the coupling strength is greatest for coupling strengths near the critical coupling strength for a fixed-point bifurcation in the corresponding semiclassical description [4]. This has significant implications for the ability to reach the zero photon state in the cavity by cooling.…”

“…In the absence of dissipation, the semiclassical equations of motion that follow for the Hamiltonian have a fixed-point pitch-fork bifurcation [4] (for bifurcation types see [5]) at a critical coupling strength of λ cr = √ ∆ω 2 . A single stable elliptic fixed point (for fixed point types see [5]), with zero cavity field amplitude below the bifurcation, changes stability to give two new elliptic fixed points with equal and opposite cavity field amplitude.…”

“…Where an analytic method is not possible to check the stability of the fixed points we discuss in the following a numerical method. Specifically, random samples are taken from a logarithmic distribution in the bounded eight-dimensional space spanned by ω, ∆, , λ, η, κ, γ , and Γ, where each parameter can take a value between 10 −4 and 10 4 . A description of a fixed point as "mostly" stable or unstable with this method will be used to indicate that the vast majority but not all (>99% but <100%) of the random samples taken yielded stable or unstable fixed points, respectively.…”

“…There is a critical coupling strength at which the nature of the ground state undergoes a qualitative change reflecting a bifurcation in a fixed point of the corresponding classical model [4]. As the coupling strength increases, the entanglement (in the ground state) between the qubit and the oscillator increases monotonically.…”

Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field

“…We do this by numerically computing the quantum steady correspondence principle has proven to be the case for other dissipative nonlinear quantum systems [31][32][33][34][35][36].…”