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Piotr Deuar

Publications and source records attributed to Piotr Deuar.

34 records · Page 2Linked to original sources
arXiv2020

Fully quantum scalable description of driven dissipative lattice models

Methods for modeling large driven dissipative quantum systems are becoming increasingly urgent due to recent experimental progress in a number of photonic platforms. We demonstrate the positive-P method to be ideal for this purpose across a wide range of parameters, focusing on the archetypal driven dissipative Bose-Hubbard model. Notably, these parameters include intermediate regimes where interactions and dissipation are comparable, and especially cases with low occupations for which common semiclassical approximations can break down. The presence of dissipation can alleviate instabilities in the method that are known to occur for closed systems, allowing the simulation of dynamics up to and including the steady state. Throughout the parameter space of the model, we determine the magnitude of dissipation that is sufficient to make the method useful and stable, finding its region of applicability to be complementary to that of truncated Wigner. We then demonstrate its use in a number of examples with nontrivial quantum correlations, including a demonstration of solving the urgent open problem of large and highly non-uniform systems with even tens of thousands of sites.

quant-ph↗
arXiv2019

A semiclassical field theory that is freed of the ultraviolet catastrophe

A more accurate semiclassical theory for ultracold gases is derived, in which the occupation of high energy modes is dynamically constrained to the Bose-Einstein distribution. This regularized version of the SGPE model preserves the proper nonlinear energy dependence of coupling to the thermal reservoir. As a result, inclusion of high energy modes above $k_BT$ does not cause a UV divergence. Instead, the reservoir becomes a constraint on the high energy tails which are included explicitly in the system. Millions of modes can be treated because computational cost scales slowly, like in other semiclassical methods. Implementations in 1d and 3d are presented, among them an accurate treatment of the famous case of the quadrupole mode (Jin et al, 1997), which had so far eluded satisfactory simulations with any field theory. Our study reveals that observed frequencies and damping of the thermal cloud depended on the experimental signal to noise ratio.

cond-mat.quant-gas↗
arXiv2019

Correlation evolution in dilute Bose-Einstein condensates after quantum quenches

The universal forms of quantum density and phase correlations after an interaction quench are found for dilute 1d, 2d, and 3d condensates. A Bogoliubov approach in a local density aproximation is used. We obtain compact expressions for the most visible effects. Our results show how loss of phase coherence and antibunching are built up after the quench by quantum fluctuations. We demonstrate further that the density correlations can be observed even with imaging resolution much worse than healing length. This indicates that the direct measurement of counterpropagating atom pairs in situ in a continuum system is realistic. The conditions in contemporary 1d experiments are especially favorable for the correlation wave observations.

cond-mat.quant-gas↗
arXiv2017

Mesoscopic density grains in the 1d interacting Bose gas from the exact Yang-Yang solution

Number fluctuations in a one-dimensional Bose gas consist of contributions from many smaller independent localized fluctuations, the density grains. We have derived a set of extended integral equations from the Yang-Yang solution for finite temperature that exactly determine all higher order moments of number fluctuations. These moments are closely related to the statistics of the localized (but not zero-range) density grains. We directly calculate the mean occupation of these fluctuations, and the variance, skewness, and kurtosis of their distribution across the whole parameter space of the gas. Findings include: Large mesoscopic density grains with a fat-tailed distribution in the thermal quasicondensate of the dilute gas and in the nonperturbative quantum turbulent regime; Regions of negative skewness and below-Gaussian kurtosis in a part of the fermionized gas, and an unexplained crossover region along $T\sim T_d/γ$; The existence of a peak in the density-density correlation function at finite interparticle spacing. We relate these density grain statistics to measurable behavior such as the statistics of coarse imaging bins, and finite-size scaling of number fluctuations. We propose how to experimentally test the relationship between thermodynamically independent density grains and density concentrations visible in single shot images.

cond-mat.quant-gas↗
arXiv2016

A tractable prescription for large-scale free flight expansion of wavefunctions

A numerical recipe is given for obtaining the density image of an initially compact quantum mechanical wavefunction that has expanded by a large but finite factor under free flight. The recipe given avoids the memory storage problems that plague this type of calculation by reducing the problem to the sum of a number of fast Fourier transforms carried out on the relatively small initial lattice. The final expanded state is given exactly on a coarser magnified grid with the same number of points as the initial state. An important application of this technique is the simulation of measured time-of-flight images in ultracold atom experiments, especially when the initial clouds contain superfluid defects. It is shown that such a finite-time expansion, rather than a far-field approximation is essential to correctly predict images of defect-laden clouds, even for long flight times. Examples shown are: an expanding quasicondensate with soliton defects and a matter-wave interferometer in 3D.

cond-mat.quant-gas↗
arXiv2016

Quantum fluctuation effects on the quench dynamics of thermal quasicondensates

We study the influence of quantum fluctuations on the phase, density, and pair correlations in a trapped quasicondensate after a quench of the interaction strength. To do so, we derive a description similar to the stochastic Gross-Pitaevskii equation (SGPE) but keeping a fully quantum description of the low-energy fields using the positive-P representation. This allows us to treat both the quantum and thermal fluctuations together in an integrated way. A plain SGPE only allows for thermal fluctuations. The approach is applicable to such situations as finite temperature quantum quenches, but not equilibrium calculations due to the time limitations inherent in positive-P descriptions of interacting gases. One sees the appearance antibunching, the generation of counter-propagating atom pairs, and increased phase fluctuations. We show that the behavior can be estimated by adding the T=0 quantum fluctuation contribution to the thermal fluctuations described by the plain SGPE.

cond-mat.quant-gas↗
arXiv2015

Classical field records of a quantum system: their internal consistency and accuracy

We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in 1d, 2d, and 3d by a careful study of the ideal gas limit. Numerical benchmarking in 1d shows that the ideal gas results carry over unchanged into the weakly interacting gas. The optimum high energy cutoff is in general shown to depend strongly on the observable in question (e.g. energy, density fluctuations, phase coherence length, condensate fraction). This explains the wide spread of past results. A consistent classical field representation with less than 10% deviation in all typical observables can be given for systems at temperatures below 0.0064 degeneracy temperature in 1d, and 0.49 critical temperature in 3d. Surprisingly, this is not possible for the 2d ideal gas even at zero temperature because mean density, density fluctuations and energy cannot be simultaneously matched to the quantum results.

cond-mat.quant-gas↗
arXiv2014

Anisotropy in s-wave Bose-Einstein condensate collisions and its relationship to superradiance

We report the experimental realization of a single-species atomic four-wave mixing process with BEC collisions for which the angular distribution of scattered atom pairs is not isotropic, despite the collisions being in the $s$-wave regime. Theoretical analysis indicates that this anomalous behavior can be explained by the anisotropic nature of the gain in the medium. There are two competing anisotropic processes: classical trajectory deflections due to the mean-field potential, and Bose enhanced scattering which bears similarity to super-radiance. We analyse the relative importance of these processes in the dynamical buildup of the anisotropic density distribution of scattered atoms, and compare to optically pumped super-radiance.

cond-mat.quant-gas↗
arXiv2013

Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques

We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. The new representation is superior in practice to an earlier phase space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times several fold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse field Ising model in one and two dimensions

cond-mat.stat-mech↗
arXiv2010

Sub-Poissonian number differences in four-wave mixing of matter waves

We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub shot-noise interferometry and studies of Einstein-Podolsky-Rosen-type nonlocality tests.

cond-mat.quant-gas↗
arXiv2010

Spontaneous Four-Wave Mixing of de Broglie Waves: Beyond Optics

We investigate the atom-optical analog of degenerate four-wave mixing of photons by colliding two Bose-Einstein condensates (BECs) of metastable helium and measuring the resulting momentum distribution of the scattered atoms with a time and space resolved detector. For the case of photons, phase matching conditions completely define the final state of the system, and in the case of two colliding BECs, simple analogy implies a spherical momentum distribution of scattered atoms. We find, however, that the final momenta of the scattered atoms instead lie on an ellipsoid whose radii are smaller than the initial collision momentum. Numerical and analytical calculations agree well with the measurements, and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.

cond-mat.quant-gas↗
arXiv2009

Simulation of complete many-body quantum dynamics using controlled quantum-semiclassical hybrids

A controlled hybridization between full quantum dynamics and semiclassical approaches (mean-field and truncated Wigner) is implemented for interacting many-boson systems. It is then demonstrated how simulating the resulting hybrid evolution equations allows one to obtain the full quantum dynamics for much longer times than is possible using an exact treatment directly. A collision of sodium BECs with 1.x10^5 atoms is simulated, in a regime that is difficult to describe semiclassically. The uncertainty of physical quantities depends on the statistics of the full quantum prediction. Cutoffs are minimised to a discretization of the Hamiltonian. The technique presented is quite general and extension to other systems is considered.

cond-mat.other↗
arXiv2005

First-principles quantum simulations of many-mode open interacting Bose gases using stochastic gauge methods

Many-mode interacting Bose gases (1D,2D,3D) are simulated from first principles. The model uses a second-quantized Hamiltonian with two-particle interactions (possibly ranged), external potential, and interactions with an environment, with no further approximations. Simulations are of a set of stochastic equations that in the limit of many realizations correspond exactly to the full quantum evolution. These are obtained using the stochastic gauge method (derived here), an extension of the positive P phase-space representation. The systems investigated are: 1) Dynamics of spatial correlations in uniform 1D and 2D Bose gases after the rapid appearance of significant two-body collisions (e.g. after entering a Feshbach resonance). 2) Dynamics of stimulated Bose enhancement of scattered atom modes during the collision of two Bose-Einstein condensates with a mean of 150 000 atoms. 3) Dynamics of trapped bosons, where the size of the trap is of the same order as the range of the interparticle potential. 4) Grand canonical thermodynamics of uniform 1D Bose gases for a variety of temperatures and collision strengths. Observables calculated include 1st-3rd order spatial correlation functions (including finite separation) and momentum distributions. The stochastic gauge method is derived, and its application to interacting Bose gases investigated in detail. It is found to improve simulation effectiveness under many conditions, and to be capable of overcoming instability and boundary term problems. Additionally, conditions under which very generalized phase-space represntations can be used to obtain tractable many-body simulations are analysed.

cond-mat.other↗
arXiv2004

The time-reversal test for stochastic quantum dynamics

The calculation of quantum dynamics is currently a central issue in theoretical physics, with diverse applications ranging from ultra-cold atomic Bose-Einstein condensates (BEC) to condensed matter, biology, and even astrophysics. Here we demonstrate a conceptually simple method of determining the regime of validity of stochastic simulations of unitary quantum dynamics by employing a time-reversal test. We apply this test to a simulation of the evolution of a quantum anharmonic oscillator with up to $6.022\times10^{23}$ (Avogadro's number) of particles. This system is realisable as a Bose-Einstein condensate in an optical lattice, for which the time-reversal procedure could be implemented experimentally.

quant-ph↗
arXiv2001

Concurrence in arbitrary dimensions

We argue that a complete characterisation of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multi-dimensional generalizations of concurrence and find evidence that they may provide useful tools for the analysis of quantum correlations in mixed bipartite states. We also introudce {\it biconcurrence} that leads to a necessary and sufficient condition for separability.

quant-ph↗