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

Abstract

Abstract. We present a theoretical description of a system of many spins strongly coupled to a bosonic chain. We rely on the use of a spinwave theory describing the Gaussian fluctuations around the mean-field solution, and focus on spin-boson chains arising as a generalization of the Dicke Hamiltonian. Our model is motivated by experimental setups such as trapped ions, or atoms/qubits coupled to cavity arrays. This situation corresponds to the cooperative (E⊗β) Jahn-Teller distortion studied in solid-state physics. However, the ability to tune the parameters of the model in quantum optical setups opens up a variety of novel intriguing situations. The main focus of this paper is to review the spin-wave theoretical description of this problem as well as to test the validity of mean-field theory. Our main result is that deviations from mean-field effects are determined by the interplay between magnetic order and mesoscopic cooperativity effects, being the latter strongly size-dependent.

Adiabatic quantum metrology with strongly correlated quantum optical systems

“…Note that this equation predicts that our quantum metrological protocol allows us to measure by a single-shot measurement the sign of δ with an error of γ/N ≈ 1/(t m N) (up to logarithmic corrections), with t m the measurement time, Eq. (27). We also highlight that our method allows one to find a narrow spectral line even when the field is far-detuned.…”

“…The second pair of co-propagating lasers with frequency difference ∆ω 2,L = ω 0 − δ (ω 0 ≫ δ ) induces a twophoton Raman transition between the spin states. The Hamiltonian describing the laser-ion interaction becomes [2,27]…”

“…− ω p =c.m. | ≫ g, ω and |ω 0 + ω 2,L | ≫ Ω x , respectively [10,27]. The first condition ensures that within the motional rotating-wave approximation (r.w.a.)…”

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

“…The result is summarized in Fig. 1 where are shown the three branches of collective excitations, assuming periodic boundary conditions with nearest-neighbours bosonic tunneling t j,l = −t(δ j,l+1 + δ j,l−1 ) and bosonic dispersion ∆ k = ∆ + 2t{1 − cos(2πk/N)} [28]. The lowest-lying branch correspond to the gapless Goldstone mode ω G , which is linear for small k, i.e., ω G = c s 2πk/N + O(k 2 ) with characteristic slope c s = 2g 2 sin( θ ) t∆/(∆ 4 + 4g 4 sin 2 ( θ )).…”

The interspersed spin boson lattice model

“…At this point, let us compare our model to the Jaynes-Cummings and Rabi lattice models, which arise in coupled-cavity arrays [15,16], or trapped-ion crystals [17,18], and may be considered as particular instances of cooperative Jahn-Teller models [19]. In these models, spins only interact locally with the bosonic modes, which are in turn coupled among themselves.…”