Non-adiabatic generation of NOON states in a Tonks–Girardeau gas

Abstract

Adiabatic techniques can be used to control quantum states with high fidelity while exercising limited control over the parameters of a system. However, because these techniques are slow compared to other timescales in the system, they are usually not suitable for creating highly unstable states or performing time-critical processes. Both of these situations arise in quantum information processing, where entangled states may be isolated from the environment only for a short time and where quantum computers require high-fidelity operations to be performed quickly. Recently it has been shown that techniques like optimal control and shortcuts to adiabaticity can be used to prepare quantum states non-adiabatically with high fidelity. Here we present two examples of how these techniques can be used to create maximally entangled many-body NOON states in one-dimensional Tonks-Girardeau gases.

Generation of N00N-like interferences with two thermal light sources

“…2 TLS (δ 1 , 0) with a maximum visibility V 2 = 1/3 [see Eqs. (21), (22) and (3), respectively]. In the future, the approach might be extended to more than two emitters by carefully tailoring appropriate detection schemes so that quantum paths are isolated such that photons from each emitter collectively propagate toward different sets of detectors.…”

“…The interest in producing photonic N00N-states by superconducting systems [13][14][15][16][17] led recently to a proposal to generate double N00N-states [18]. Also other quantum systems have been explored, leading to atomic N00N-states [19][20][21][22], spin N00N-states [23], and even mechanical N00N states, implemented by entangling two mechanical microresonators [24,25]. N00N-states have been further examined in the context of fundamental investigations of quantum mechanics [26][27][28].…”

Generation of atomic NOON states via shortcuts to adiabatic passage

“…Thus, a variety of schemes have been proposed to construct shortcuts to adiabatic passage in both the theory and experiment [37][38][39][40][41][42][43]. Recently, Schloss et al proposed a scheme of shortcuts to adiabaticity used to create maximally entangled many-body NOON states in one-dimensional Tonks-Girardeau gases [44]. In this paper, we construct an effective shortcut to adiabatic passage for generating NOON states of two sets of -type three-level atoms.…”

Static and dynamic phases of a Tonks–Girardeau gas in an optical lattice

“…The observed behavior is similar to a type of quantum sprocket, where the rotating lattice will impart maximum angular momentum to the gas if the system is in the insulating phase, while in the superfluid phase only reduced momentum transfer is observed due to tunneling of the particles between lattice sites. Our work is related to recent investigations of driven cold atom systems in the continuum [33][34][35][36][37][38], and in the Bose-Hubbard model (BHM) [39][40][41][42], which is naturally connected to the continuous model in the limit of tight trapping. Another recent related work has investigated the localization properties of a TG gas in a continuum version of the Aubry-Andre model (using a bi-chromatic lattice) [43].…”