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arXiv:1708.06676 · Physical Review A

Synchronization transition in dipole-coupled two-level systems with positional disorder

M. P. Kwasigroch, Nigel R. Cooper

Published Nov 9, 2017• 21 citations
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Abstract

We study the decoherence dynamics of dipole-coupled two-level quantum systems in Ramsey-type experiments. We focus on large networks of two-level systems, confined to two spatial dimensions and with positional disorder giving rise to disordered dipolar couplings. This setting is relevant for modeling the decoherence dynamics of the rotational excitations of polar molecules confined to deep optical lattices, where disorder arises from the random filling of lattice sites with occupation probability $p$. We show that the decoherence dynamics exhibits a phase transition at a critical filling ${p}_{c}\ensuremath{\simeq}0.15$. For $p<{p}_{c}$ the dynamics is disorder dominated and the Ramsey interference signal decays on a time scale ${T}_{2}\ensuremath{\propto}{p}^{\ensuremath{-}3/2}$. For $p>{p}_{c}$ the dipolar interactions dominate the disorder, and the system behaves as a collective spin-ordered phase, representing synchronization of the two-level systems and persistent Ramsey oscillations with divergent ${T}_{2}$ for large systems. For a finite number of two-level systems $N$, the spin-ordered phase at $p>{p}_{c}$ undergoes a crossover to a collective spin-squeezed state on a time scale ${\ensuremath{\tau}}_{\mathrm{sq}}\ensuremath{\propto}\sqrt{N}$. We develop a self-consistent mean-field theory that is capable of capturing the synchronization transition at ${p}_{c}$, and provide an intuitive theoretical picture that describes the phase transition in the long-time dynamics. We also show that the decoherence dynamics appear to be ergodic in the vicinity of ${p}_{c}$, the long-time behavior being well described by the predictions of equilibrium thermodynamics. The results are supported by the results of exact diagonalization studies of small systems.

DOI
10.1103/physreva.96.053610

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We study the decoherence dynamics of dipole-coupled two-level quantum systems in Ramsey-type experiments. We focus on large networks of two-level systems, confined to two spatial dimensions and with positional disorder giving rise to disordered dipolar couplings. This setting is relevant for modeling the decoherence dynamics of the rotational excitations of polar molecules confined to deep optical lattices, where disorder arises from the random filling of lattice sites with occupation probability ppp. We show that the decoherence dynamics exhibits a phase transition at a critical filling pc\ensuremath≃0.15{p}_{c}\ensuremath{\simeq}0.15pc​\ensuremath≃0.15. For p<pcp<{p}_{c}p<pc​ the dynamics is disorder dominated and the Ramsey interference signal decays on a time scale T2\ensuremath∝p\ensuremath−3/2{T}_{2}\ensuremath{\propto}{p}^{\ensuremath{-}3/2}T2​\ensuremath∝p\ensuremath−3/2. For p>pcp>{p}_{c}p>pc​ the dipolar interactions dominate the disorder, and the system behaves as a collective spin-ordered phase, representing synchronization of the two-level systems and persistent Ramsey oscillations with divergent T2{T}_{2}T2​ for large systems. For a finite number of two-level systems NNN, the spin-ordered phase at p>pcp>{p}_{c}p>pc​ undergoes a crossover to a collective spin-squeezed state on a time scale \ensuremathτsq\ensuremath∝N{\ensuremath{\tau}}_{\mathrm{sq}}\ensuremath{\propto}\sqrt{N}\ensuremathτsq​\ensuremath∝N​. We develop a self-consistent mean-field theory that is capable of capturing the synchronization transition at pc{p}_{c}pc​, and provide an intuitive theoretical picture that describes the phase transition in the long-time dynamics. We also show that the decoherence dynamics appear to be ergodic in the vicinity of pc{p}_{c}pc​, the long-time behavior being well described by the predictions of equilibrium thermodynamics. The results are supported by the results of exact diagonalization studies of small systems.
Spin squeezed entanglement enables metrological precision beyond the classical limit. Understood through the lens of continuous symmetry breaking, dipolar spin systems exhibit the remarkable ability to generate spin squeezing via their intrinsic quench dynamics. To date, this understanding has primarily focused on lattice spin systems; in practice however, dipolar spin systems$\unicode{x2014}$ranging from ultracold molecules to nuclear spin ensembles and solid-state color centers$\unicode{x2014}$often exhibit significant amounts of positional disorder. Here, we develop a theory for scalable spin squeezing in a two-dimensional randomly diluted lattice of quantum dipoles, which naturally realize a dipolar XXZ model. Via extensive quantum Monte Carlo simulations, we map out the phase diagram for finite-temperature XY order, and by extension scalable spin squeezing, as a function of both disorder and Ising anisotropy. As the disorder increases, we find that scalable spin squeezing survives only near the Heisenberg point. We show that this behavior is due to the presence of rare tightly-coupled dimers, which effectively heat the system post-quench. In the case of strongly-interacting nitrogen-vacancy centers in diamond, we demonstrate that an experimentally feasible strategy to decouple the problematic dimers from the dynamics is sufficient to enable scalable spin squeezing.
We use Ramsey spectroscopy to experimentally probe the quantum dynamics of disordered dipolar-interacting ultracold molecules in a partially filled optical lattice, and we compare the results to theory. We report the capability to control the dipolar interaction strength. We find excellent agreement between our measurements of the spin dynamics and theoretical calculations with no fitting parameters, including the dynamics' dependence on molecule number and on the dipolar interaction strength. This agreement verifies the microscopic model expected to govern the dynamics of dipolar molecules, even in this strongly correlated beyond-mean-field regime, and represents the first step towards using this system to explore many-body dynamics in regimes that are inaccessible to current theoretical techniques.
In this thesis, we consider the forms of non-equilibrium phenomena that can arise in atoms or polar molecules trapped in a deep optical lattice and coupled by dipolar internal degrees of freedom. We specifically focus on only two internal states, which results in the systems studied behaving as spin−1/2-1/2−1/2 models with long-range interactions. We first study a closed system with both static and resonant near-field dipole interactions under an external drive. By studying the uniform mean-field dynamics of the system, we find the dynamics are given by Rabi oscillations, with a bifurcation in the dynamics as a function of drive strength between small scale and large scale oscillations. Analysing the stability of these oscillations to small fluctuations reveals that interactions tend to cause the oscillations to decohere. However, we find parameter regimes where coherent oscillations can persist for high enough intensity drive. We then consider the effects of an environment on the non-equilibrium dynamics of the near-field dipole model. We find that within the mean-field approximation, an environment causes the system to relax to many novel steady state spin configurations, such as spin density waves, antiferromagnetism and long-time oscillations, as well as bistabilities between these phases. To assess the validity of the mean-field approximation, we compare our mean-field results to small quantum systems. We carry out a similar analysis on a system with far-field dipole interactions, where it is necessary to introduce nonlocal dissipation, which results in several decay modes into the environment. These decay modes lead to instabilities of many of the steady state phases that occurred in the near-field dipole system, leading to the emergence of more spin density wave and oscillatory phases. Finally, we examine the dynamics on the approach to steady state in a dissipative dipolar system by studying Rydberg atoms coupled to a photonic crystal waveguide, which mediates an effective dipole-dipole interaction between the atoms. We find that if two excitations exist in the system, then bound states can form, with nonlocal dissipation resulting in a momentum dependent decay rate of the bound states and also greater freedom in engineering the bound state energy dispersion.
We consider the dynamics of rotational excitations placed on a single molecule in spatially disordered 1D, 2D and 3D ensembles of ultracold molecules trapped in optical lattices. The disorder arises from incomplete populations of optical lattices with molecules. This leads to a model corresponding to a quantum particle with long-range tunnelling amplitudes moving on a lattice with the same on-site energy but with forbidden access to random sites (vacancies). We examine the time and length scales of Anderson localization for this type of disorder with realistic experimental parameters in the Hamiltonian. We show that for an experimentally realized system of KRb molecules on an optical lattice this type of disorder leads to disorder-induced localization in 1D and 2D systems on a time scale t∼1t \sim 1t∼1 sec. For 3D lattices with 555555 sites in each dimension and vacancy concentration $ 90~\%$, the rotational excitations diffuse to the edges of the lattice and show no signature of Anderson localization. We examine the role of the long-range tunnelling amplitudes allowing for transfer of rotational excitations between distant lattice sites. Our results show that the long-range tunnelling has little impact on the dynamics in the diffusive regime but affects significantly the localization dynamics in lattices with large concentrations of vacancies, enhancing the width of the localized distributions in 2D lattices by more than a factor of 2. Our results raise a general question whether quantum particles with long-range tunnelling can undergo quantum localization in 3D lattices with substitutional disorder.
Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths and pronounced separation of dynamical timescales. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization generates an effective detuning that suppresses transfer to other weakly coupled sites, yielding a parametrically enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.
We theoretically investigate the out-of-equilibrium dynamics of irregular one- and two-dimensional arrays of Rydberg dipoles featuring spatially anisotropic interactions. Starting from a collectively polarized initial state, we map out the dynamical phase diagram and identify a crossover between regimes of regular and anomalously slow relaxation of the initial collective order that strongly depends on both the degree of interaction disorder and anisotropy. In addition, we find that the regime of slow relaxation is characterized by a subballistic propagation of correlations that remained confined to short distances even at long times. To explain our findings we develop an analytic model based on decoupled clusters of interacting dipoles that goes beyond prior theoretical works and enables us to identify multiple relaxation timescales. Our findings can be relevant for a wide variety of quantum science platforms naturally featuring disordered dipolar interactions, including polar molecules, frozen Rydberg gases, and nitrogen-vacancy centers.