Quantum Simulation of the Cooperative Jahn-Teller Transition in 1D Ion Crystals

Abstract

The Jahn-Teller effect explains distortions and nondegenerate energy levels in molecular and solid-state physics via a coupling of effective spins to collective bosons. Here we propose and theoretically analyze the quantum simulation of a many-body Jahn-Teller model with linear ion crystals subjected to magnetic field gradients. We show that the system undergoes a quantum magnetic structural phase transition which leads to a reordering of particle positions and the formation of a spin-phonon quasicondensate in mesoscopic ion chains.

Mesoscopic mean-field theory for spin-boson chains in quantum optical systems

“…This effect has received attention for its connections with high-Tc superconductivity and colossal magnetoresistance [18,19,20]. Very recently it was shown that a generalization of interaction (1) can be implemented in a quite natural way in a linear ion crystal placed in a magnetic field gradient [21,22]. The prospects for experimental investigation of the cooperative Jahn-Teller effect would be very interesting, since they would allow us to observe novel quantum structural phase transitions in clean controllable systems.…”

Collective Modes in the Cooperative Jahn–Teller Model: Path Integral Approach

“…(25) and keep only the quadratic terms of the density fluctuations. The latter condition can be fulfilled for large coupling g ≫ g c (ρ ≫ 1), where the quantum fluctuations are suppressed [11]. Assuming that the spin and bosonic fields vary smoothly on the scale of lattice constant a in a d dimensional cubic lattice one can perform gradient expansion, such that in the symmetry broken phase g > g c the continuum action becomes…”

“…The spins are implemented by the internal two metastable levels of the trapped ions where ω z is the effective spin frequency. The desired Jahn-Teller coupling can be realized by the interaction of the spins with an oscillating magnetic field gradient [11,12]. Alternative realization of the Jahn-Teller coupling is based on the interaction of the ions with laser beams propagating in two orthogonal directions tuned near the respective red and blue sidebands [19].…”

“…Here we emphasize that for a linear ion crystal with positive hopping amplitude the saddle-point approximation is not applied straightforward. This problem can be overcome by applying a canonical transformation to the operatorsâ ε, j → (−1) jâ ε, j and σ ε j → (−1) j σ ε j in (1) [11,27]. After this transformation to the staggered spin-boson basis the cJT model (1) is unchanged, but the tunneling is modified to t stagg j,l = (−1) j−l t j,l .…”

“…Furthermore, the collective effects induced by the Jahn-Teller coupling may explain the transition of some solids, such as fullerene compounds, to high-temperature superconductors [10]. With the current quantum optical technologies the cJT model can be realized in laser or magnetically driven ion crystal [11,12] and cavity/circuit QED systems based on superconducting qubits in transmission line resonators [13,14]. Here we focus on E ⊗ e Jahn-Teller model which possess continuous U(1) symmetry.…”