[Paper Review] Dynamical creation and detection of entangled many-body states in a chiral atom chain

Giuseppe Buonaiuto, Ryan Jones+2 more|arXiv (Cornell University)|Feb 22, 2019

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper proposes using photon counting statistics in guided modes to dynamically detect and characterize entangled many-body states in a chiral atom chain coupled to a waveguide. By analyzing the scaled cumulant generating function (SCGF) of emitted photons, the method reveals dark entangled states and enables in-situ probing of complex dynamical behavior, including coexistence between entangled and mixed phases, even under experimental imperfections like unguided photon emission.

ABSTRACT

Open quantum systems with chiral interactions can be realized by coupling atoms to guided radiation modes in waveguides or optical fibres. In their steady state these systems can feature intricate many-body phases such as entangled dark states, but their detection and characterization remains a challenge. Here we show how such collective phenomena can be uncovered through monitoring the record of photons emitted into the guided modes. This permits the identification of dark entangled states but furthermore offers novel capabilities for probing complex dynamical behavior, such as the coexistence of a dark entangled and a mixed phase. Our results are of direct relevance for current experiments, as they provide a framework for probing, characterizing and classifying dynamical features of chiral light-matter systems.

Motivation & Objective

• To develop a method for detecting and characterizing entangled many-body states in chiral atom chains coupled to waveguides.
• To address the experimental challenge of identifying dark entangled states that are otherwise difficult to probe due to their decoherence protection.
• To explore the dynamical behavior of chiral light-matter systems, particularly the coexistence of entangled dark and mixed phases.
• To assess the robustness of these detection methods under realistic imperfections, such as emission into unguided modes.
• To establish a framework linking photon emission statistics to the underlying quantum state of the atom chain for use in quantum simulation and information processing.

Proposed method

• The study employs the scaled cumulant generating function (SCGF) formalism to analyze the counting statistics of photons emitted into left and right guided modes of a waveguide.
• The SCGF is used to extract the biased quantum state, which reveals the effective dynamics under photon counting, enabling identification of dark and mixed phases.
• The Lindblad master equation models the open quantum dynamics of the atom chain, including coherent laser driving, chiral dipole-dipole interactions via guided modes, and spontaneous emission into unguided modes.
• The method incorporates the large deviation principle to connect photon statistics to the steady-state properties of the many-body system.
• Numerical simulations are performed for two detuning patterns: uniform and alternating, to probe distinct many-body phases.
• The approach is validated by showing that characteristic features in the photon emission rate and purity of the biased state directly signal the presence of dark entangled states or phase coexistence.

Experimental results

Research questions

• RQ1 Can photon counting statistics in guided modes be used to detect and characterize entangled many-body states in a chiral atom chain?
• RQ2 How does the SCGF formalism enable the identification of dark entangled states and their dynamical fluctuations?
• RQ3 What happens to the detection of entangled states when unguided photon emission is introduced as an experimental imperfection?
• RQ4 Can the coexistence of a dark entangled phase and a mixed phase be observed and characterized through photon statistics?
• RQ5 How does the system's dynamical behavior change under different detuning patterns, such as alternating vs. uniform detuning?

Key findings

• The SCGF of photon emission reveals a sharp transition between a dark entangled phase and a mixed phase, with the former corresponding to a pure dimerized state.
• For uniform detuning, the system exhibits a clear phase transition: the dark state is stable and detectable via photon statistics, while increasing unguided emission rate $Γ$ gradually suppresses the sharp features in the SCGF.
• For alternating detuning, a pure dimer dark state emerges only as a fluctuation in an intermittent photon emission dynamics when unguided emission is present, even though the steady state becomes mixed.
• The purity of the biased state drops with increasing unguided emission rate, indicating a transition toward a mixed phase, but the characteristic features of the SCGF persist as signatures of dynamical coexistence.
• The photon emission record shows intermittent behavior in the alternating detuning case with small $Γ$, which is a direct experimental signature of the coexistence of a dark entangled phase and a mixed phase.
• The analytical form of the dark dimer state is derived as $\rho_{\mathrm{dimer}} = \bigotimes_{j=1}^{N/2} \ket{D}_{2j-1,2j}\bra{D}$, with $\ket{D} \propto \ket{gg} + \beta(\ket{ge} - \ket{eg})$, where $\beta = -2\Omega/(2\delta + i\Delta\gamma)$.