Session M28: Nonequilibrium and Strongly Interacting Ultracold Matter

Live

The theoretical framework of supersymmetric quantum mechanics (SUSY-QM) has found many applied physics applications, especially in photonics. We use SUSY-QM to address the micro-bending issue in optical fibers. Micro-bending is caused by undesirable interactions in fiber cables, leading to signal loss in communication networks. Starting with a refractive index profile for a planar optical waveguide, we use the formalism presented in Ref. [1] to model the micro-bending attenuation by a Fokker-Planck equation. The planar waveguide is a preliminary model for future analysis of optical fibers. We then apply the SUSY-QM transformation to the Fokker-Planck equation to find a new refractive index profile with a different micro-bending attenuation profile. We observe that for a broad class of monomial refractive index profiles, including the conventional parabolic profile, it is always possible to obtain an index profile with a larger micro-bending attenuation. However, obtaining a smaller attenuation is not always possible and is restricted to a subset of index profiles. We identify this subset [2].

[1] M. Rousseau, J. Arnaud, Opt. Commun. 25, 333 (1978).
[2] S. Ward, R. Allahverdi, A. Mafi, arXiv:2009.11847.   

Live

We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension associated with boundary-to-boundary correlation functions survives the truncation of approximating the continuum hyperbolic space with a lattice. In the 2d case we incorporate quantum gravity effects by allowing dynamical fluctuation of the tessellation   

Live

The problem of the back-reaction (BR) has its roots in the field of gravity but, nevertheless, is a general concept and relevant to a wide range of physical systems. It aims towards a self-consistent theory of the interaction between a quantum field and its background.

We pursue the study of the BR within the framework of optomechanics and analog models. (i) In the former case, we consider an optical cavity enclosed by a freely moving mirror. In this case the BR is exerted onto the moving mirror by the particles created in the cavity because of the dynamic Casimir effect. This results in an effective damping experienced by the mirror. We investigate the quantum fluctuations of such friction force, as well as their consequences on the quantum state of the mirror. (ii) In the latter case, a time dependent background is implemented by considering a non-stationary Bose-Einstein condensate (BEC). We simulate the phenomenon of the Pre-Heating in the early Universe by using an elongated condensate, that is let to oscillate in its transverse direction by exciting one (or more) of the corresponding (high-energy) modes. We observe the amplification of the vacuum fluctuations in the (low-energy) longitudinal modes and the damping of the transverse modes.   

Live

Analogue gravity enables the study of fields on curved spacetimes in the laboratory. There are numerous experimental platforms in which amplification at the event horizon or the ergoregion has been observed. For example, polaritons in semiconductor microcavities may be made to behave as “fluids of light” and their flow can be engineered to create various geometries with, eg horizons and ergosurfaces. In this talk, I briefly review the physics of fluids of light with polaritons and then explain how to create a polariton flow analogous to the curved spacetime of a rotating black hole by generating a large vortex.
I then discuss experimental results on the propagation of dark solitons on this vortex and show how to theoretically describe their motion with field theory on curved spacetime. This opens up a discussion on the comparison between this description and actual lab data, which informs generic issues in analogue gravity experiments and promises access to phenomena beyond the established field theory such as dynamical instabilities and back-reaction of the spacetime onto emission.   

Live

The q-state clock model is a classical spin model that corresponds to the Ising model (when q = 2) and the XY model (when q goes to infinity). The integer-q clock model has been studied extensively and has been shown to have a single phase transition when q = 2,3,4 and two phase transitions when q > 4. We investigate a class of clock models for non-integer q using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with non-integer q has two phase transitions with one of them possibly in the Ising universality class. In this model, thermodynamic quantities appear to vary smoothly with q as q approaches an integer from below. However, the appearance of an additional spin state when q crosses an integer results in an abrupt change in the thermodynamic quantities. The model with non-integer q serves as a testbed for TRG methods and has interesting features which already appear at small lattice sizes, making this model a candidate for study on near-term quantum simulators and in particular Rydberg atom devices.   

Live

A concrete experimental setup for quantum simulating the (1+1)d Abelian Higgs model has been proposed in J. Zhang et al. (2018), where the Hamiltonian in the plaquette quantum number (quantized electric field) representation can be implemented on a multi-leg ladder with a single atom each rung. The finite size scaling of the energy gap can be measured and its universal behavior extracted at large enough spin truncation. However the O(2) limit of this representation has no real BKT transition for any finite spin truncation, and properties of matter fields cannot be measured directly. We study the Hamiltonian in the link quantum number (charge) representation in detail with density matrix renormalization group. We find that the BKT transition in the O(2) limit is present in the smallest spin truncation (spin-1). The gap scaling to locate the BKT transition point and parameters b, C are studied for different spin truncations. We find universal functions relating the mass gap, the gauge coupling, and the spatial size in the smallest spin truncation, which does not exist in the field representation. We study the effect of g ∼ 1/N_s perturbing the BKT phase. The results for SU(2) spin operators are also compared. Possible experimental realization is also discussed.   

Live

The classical O(2) model on a Euclidean space time can be obtained as the zero gauge coupling limit of scalar QED. This is a dual representation where the plaquette (field) quantum numbers determine the charge quantum numbers on the links according to Gauss's law. Alternatively, we can use the original charge representation of the O(2) model. Taking the time continuum limit, we study the spectra of the Hamiltonians in the two representations with a truncation to "spin S", where the quantum numbers have an absolute value less or equal to S. In the infinite S limit the spectra are identical however for quantum simulations, truncations are needed. The field representation is always gapped with finite spin truncations, while the charge representation preserves the BKT transition even for the smallest spin truncation S = 1. In the charge representation, the Hamiltonian with truncated exp( ±iθ) operators has the BKT critical point that converges exponentially with S, while that with SU(2) S^± has only algebraic convergence like 1/S² for the BKT point. The field representation can recover the gap scaling in the charge representation by gapping out the states that have a charge bigger than S.   

Live

Based on a generalization of Hohenberg-Kohn’s theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix γ as a variable but still recovers quantum correlations in an exact way it is particularly well suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying v-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals F[γ] for this N-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. For Bose-Einstein condensates, the respective gradient forces are found to diverge, providing a comprehensive explanation for the absence of complete condensation in nature.

CL Benavides-Riveros, J Wolff, MAL Marques, and C Schilling, Phys. Rev. Lett. 124, 180603 (2020).   

Live

A key problem in describing the dynamics of an interacting system starting from initial states with non-trivial connected correlations is that Wick's theorem is no longer valid in this system. We show that Wick's theorem and resultant other structures of interacting field theories can be restored in such a situation for fermions if one considers additional interaction vertices related to the initial correlations. We use this to study how the evolution of one particle correlations in a Hubbard model is affected by initial correlations in the system.   

Live

We discuss an application of our new machine learning toolbox, the
Universal Neural-Network Interface for Quantum Observable Readout from
N-body wavefunctions (UNIQORN, https://arxiv.org/abs/2010.14510 ).
We follow a strategy that is inverse to density functional theory: we
infer the potential that a many-body system of indistinguishable bosonic
particles is placed in from absorption or single-shot images, i.e.,
samples of the N-body state.
We demonstrate the network’s ability to correctly learn and generalize
from such images in both real and momentum space. We thus open up new
possibilities for the analysis of experimental single-shot images.
The connection between the single-shot measurements and the inferred
potential is investigated further in a comparison to potentials obtained
via the Thomas Fermi (TF) approximation. The potentials inferred with
our model are shown to be significantly more accurate than its TF
counterparts. We plan to deploy our machine learning models for
experimental data in the future.   

Live

I will present a theoretical study of the dynamics of a Bose-Einstein condensate (BEC) trapped inside an expanding toroid that can realize an analogue inflationary universe. As the system expands, the phonons in the BEC undergo redshift and damping due to quantum pressure effects. This rapidly expanding toroidal BEC can exhibit spontaneous particle creation, that can be studied in the context of an initial coherent state wavefunction. Finally, I discuss how particle creation would be revealed in the atom density and density correlations.

A. Bhardwaj, D. Vaido & D. E. Sheehy, arXiv:2009.05611   

Live

Trapped ion systems are a leading candidate for demonstrating the viability of scalable Quantum Computers (QCs). 1D ion arrays in linear RF traps are a dependable workhorse in this effort, but going to 2 dimensions may be useful and interesting for scaling up the system, and for some quantum simulations.Compared to their 1D counterparts, where the ions can be localized near the RF null to minimize micromotion, in 2D systems the excess micromotion is unavoidable. Micromotion is driven motion that is synchronous with the trapping RF field in a Paul trap. Large micromotion amplitude can impact ionic normal mode structure and laser cooling efficiency. Understanding micromotion and its undesirable effects is a critical step toward using 2D trapped ion crystals as a QC platform.We present Molecular Dynamics (MD) simulations of a trap specifically designed for trapping 2D crystals to examine the effects of micromotion on crystal configuration stability, laser cooling and melting dynamics in 2D. In our simulated ion trajectories, initial results depict the effects of excess micromotion. In order to match or inform experimental setup to eventually minimize micromotion effects, we are probing optimal adjustments to parameters used in our simulations via symmetry and transitions clues.   

Not Participating

Quantum thermalization, i.e., how an isolated quantum system can dynamically reach thermal equilibrium behavior, is a long-standing problem of quantum statistics. The eigenstate thermalization hypothesis (ETH) poses that, under certain conditions, the long-time expectation value w.r.t. a typical energy eigenstate is indistinguishable from a microcanonical average. This precludes describing the dynamical approach to equilibrium. By contrast, in a sufficiently complex, nonintegrable system (characterized by a vast Hilbert space dimension D), any experiment defines a partitioning into the measured quantum numbers and the remaining Hilbert subspace. The entanglement entropy of this measured system reaches a maximum by tracing out the unobserved subspace, which acts as a grand-canonical bath [Ann. Phys. 1700124 (2018)]. We find, that the approach to the thermodynamic limit is controled by the size of D rather than the particle number. We show thermalization and grand-canonical behavior of fluctuations for a bose gas and for small Fermi-Hubbard clusters. For the latter, we consider spin and charge as the subsystems in the above sense and investigate the temperature dynamics. They are well described by rate equations for spin and charge temperatures with an exponential memory kernel.   

On Demand

The Rabi model describes the simplest nontrivial interaction between a few-level system and a bosonic mode, featuring in multiple seemingly unrelated systems of importance to quantum science and technology. While exact expressions for the energies of this model and its few-mode extensions have been obtained, they involve roots of transcendental functions and are thus cumbersome and unintuitive. Utilizing the symmetric generalized rotating wave approximation (S-GRWA), we develop a family of approximations for the energies of the two-mode two-photon Rabi model. The simplest elements of the family are analytically tractable and physically intuitive, providing good approximations in regimes of interest such as ultra- and deep-strong coupling. Higher-order approximate energies can be used if more accuracy is required.   

On Demand

We explore the nonequilibrium quantum heat transport of a nonlinear bosonic system in the presence of hyper-parametric oscillation, using degenerate spontaneous four-wave mixing (SFWM) occurring in two cavities. We estimate thermodynamic response analytically by constructing su(2) algebra of nonlinear Hamiltonian and predict that the system exhibits the negative energy gap mode. Excitation mode including a non-uniform energy gap with the ground-state transition in this specific form of the interaction causes the transition of transient heat current enabling the system to cool down, and mode mixing effect unlike pure linear coupling in the presence of symmetric coupling between the system and the bath. We then show this numerically for single and two baths cases by considering the non-equilibrium situation and obtain the notion of mode mixing effect in the appearance of the metastable state by comparing the thermodynamic response of a generic nonlinear interactions, e.g., Bose-Hubbard type interaction induced via cross-phase modulation (XPM). We believe that SFWM in the strong-coupling regime can be applicable to initialize of the quantum state exhibiting quantum coherence by the cooling process.