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We investigate the squeezing of ultrashort pulses using self-induced transparency in a mercury-filled hollow-core photonic crystal fiber. Our focus is on quadrature squeezing at low mercury vapor pressures, with atoms near resonance on the $^3{\rm D}_3 \to 6^3{\rm P}_2$ transition. We vary the atomic density, thus the gas pressure (from 2.72 to 15.7$\mu$bar), by adjusting the temperature (from 273~K to 303 ~K). Our results show that achieving squeezing at room temperature, considering both fermionic and bosonic mercury isotopes, requires ultrashort femtosecond pulses. We also determine the optimal detection length for squeezing at different pressures and temperatures.

We study the quantum squeezing produced in self-induced transparency in a photonic crystal fiber by performing a fully quantum simulation based on the positive $P$ representation. The amplitude squeezing depends on the area of the initial pulse: when the area is $2\pi$, there is no energy absorption and no amplitude squeezing. However, when the area is between 2$\pi$ and 3$\pi$, one observes amplitude-dependent energy absorption and a significant amount of squeezing. We also investigate the effect of damping and temperature: the results indicate that a heightened atom-pulse coupling, caused by an increase in the spontaneous emission ratio reduces the amplitude squeezing., Comment: 8 pages, 5 figures

Bright squeezed light can be generated in optical fibers utilizing the Kerr effect for ultrashort laser pulses. However, pulse propagation in a fiber is subject to nonconservative effects that deteriorate the squeezing. Here, we analyze two-mode polarization squeezing, which is SU(2)-invariant, robust against technical perturbations, and can be generated in a polarization-maintaining fiber. We perform a rigorous numerical optimization of the process and the pulse parameters using our advanced model of quantum pulse evolution in the fiber that includes various nonconservative effects and real fiber data. Numerical results are consistent with experimental results., Comment: 9 pages, 3 figures

Out-of-time-order correlators (OTOCs) have proven to be a useful tool for studying thermalisation in quantum systems. In particular, the exponential growth of OTOCS, or scrambling, is sometimes taken as an indicator of chaos in quantum systems, despite the fact that saddle points in integrable systems can also drive rapid growth in OTOCs. By analysing the Dicke model and a driven Bose-Hubbard dimer, we demonstrate that the OTOC growth driven by chaos can, nonetheless, be distinguished from that driven by saddle points through the long-term behaviour. Besides quantitative differences in the long-term average, the saddle point gives rise to large oscillations not observed in the chaotic case. The differences are also highlighted by entanglement entropy, which in the chaotic driven dimer matches a Page curve prediction. These results illustrate additional markers that can be used to distinguish chaotic behaviour in quantum systems, beyond the initial exponential growth in OTOCs., Comment: 7 pages, 5 figures

In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically evolving state that are correlated with the presence of chaos in the classical limit. We propose the statistical distance between initially similar number distributions as a reliable measure to distinguish regular from chaotic behaviour in the quantum dynamics. Besides being experimentally accessible, number distributions can be efficiently reconstructed numerically from binned phase-space trajectories in a truncated Wigner approximation. Although the evolving Wigner function becomes very irregular in the chaotic regions, the truncated Wigner method is nevertheless able to capture accurately the beyond mean-field dynamics., Comment: 10 pages, 10 figures

Many-site Bose-Hubbard lattices display complex semiclassical dynamics, with both chaotic and regular features. We have characterised chaos in the semiclassical dynamics of short Bose-Hubbard chains using both stroboscopic phase space projections and finite-time Lyapunov exponents. We found that chaos was present for intermediate collisional nonlinearity in the open trimer and quatramer systems, with soft chaos and Kolmogoroff-Arnold-Moser islands evident. We have found that the finite-time Lyapunov exponents are consistent with stroboscopic maps for the prediction of chaos in these small systems. This gives us confidence that the finite-time Lyapunov exponents will be a useful tool for the characterisation of chaos in larger systems, where meaningful phase-space projections are not possible and the dimensionality of the problem can make the standard methods intractable., Comment: 15 pages, 8 figures

We provide the necessary framework for carrying out stochastic positive-P and gauge-P simulations of bosonic systems with long range interactions. In these approaches, the quantum evolution is sampled by trajectories in phase space, allowing calculation of correlations without truncation of the Hilbert space or other approximations to the quantum state. The main drawback is that the simulation time is limited by noise arising from interactions. We show that the long-range character of these interactions does not further increase the limitations of these methods, in contrast to the situation for alternatives such as the density matrix renormalisation group. Furthermore, stochastic gauge techniques can also successfully extend simulation times in the long-range-interaction case, by making using of parameters that affect the noise properties of trajectories, without affecting physical observables. We derive essential results that significantly aid the use of these methods: estimates of the available simulation time, optimized stochastic gauges, a general form of the characteristic stochastic variance and adaptations for very large systems. Testing the performance of particular drift and diffusion gauges for nonlocal interactions, we find that, for small to medium systems, drift gauges are beneficial, whereas for sufficiently large systems, it is optimal to use only a diffusion gauge. The methods are illustrated with direct numerical simulations of interaction quenches in extended Bose-Hubbard lattice systems and the excitation of Rydberg states in a Bose-Einstein condensate, also without the need for the typical frozen gas approximation. We demonstrate that gauges can indeed lengthen the useful simulation time., Comment: 19 pages, 11 appendix, 3 figures

Comment on a letter to Nature Physics, where Sakmann and Kasevich claim to solve the many-body time dependent Schr\"odinger equation to simulate single experimental runs of interacting quantum systems., Comment: Sent to Nature Physics as correspondence

The use of an electron beam to remove ultracold atoms from selected sites in an optical lattice has opened up new opportunities to study transport in quantum systems [R. Labouvie {\it et al.\ }, Phys.\ Rev.\ Lett.\ {\bf 115}, 050601 (2015)]. Inspired by this experimental result, we examine the effects of number difference, dephasing, and initial quantum statistics on the filling of an initially depleted middle well in the three-well inline Bose-Hubbard model. We find that the well-known phenomenon of macroscopic self-trapping is the main contributor to oscillatory negative differential conductivity in our model, with phase diffusion being a secondary effect. However, we find that phase diffusion is required for the production of direct atomic current, with the coherent process showing damped oscillatory currents. We also find that our results are highly dependent on the initial quantum states of the atoms in the system., Comment: 9 figures, 6 pages

Labouvie \etal (\prl {\bf 115}, 050601, (20015)) recently demonstrated negative differential conductivity (NDC) in a multi-well Bose-Einstein condensate. They stated "we demonstrate that NDC originates from a nonlinear, atom number dependent tunneling coupling in combination with fast collisional decoherence." We show theoretically how the essential feature of NDC, a reduction in atomic current caused by an increase in chemical potential, is present in unitary dynamics through the well-known mechanism of macroscopic self-trapping (MST), and that the collisional decoherence merely serves as a quantitative modification of this., Comment: Submitted as a comment. A more extensive article is in preparation

We examine one asymmetric adnd two fully symmetric Gaussian continuous-variable systems in terms of their tripartite and bipartite entanglement properties. We treat pure states and are able to find analytic solutions using the undepleted pump approximation for the Hamiltonian models, and standard beamsplitter relations for a model that mixes the outputs of optical parametric oscillators. Our two symmetric systems exhibit perfect tripartite correlations, but only in the unphysical limit of infinite squeezing. For more realistic squeezing parameters, all three systems exhibit both tripartite and bipartite entanglement. We conclude that none of the outputs are completely analogous to either GHZ or W states, but there are parameter regions where they produce T states introduced by Adesso \etal The qualitative differences in the output states for different interaction parameters indicate that continuous-variable tripartite quantum information systems offer a versatility not found in bipartite systems., Comment: 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:1510.01821

Non-Gaussian correlations in a pure state are inextricably linked with non-classical features, such as a non positive-definite Wigner function. In a commonly used simulation technique in ultracold atoms and quantum optics, known as the truncated Wigner method, the quantum dynamics is mapped to stochastic trajectories in phase space, governed by a positive approximation to the true Wigner distribution. The question thus arises: how accurate is this approach in predicting truly non-classical behaviour? In this article, we benchmark the ability of the truncated Wigner phase-space method to reproduce the non-Gaussian statistics of the single mode anharmonic oscillator. We find that the this method can reliably predict departures from Gaussian statistics over a wide range of particle numbers, whereas the positive-P representation method, which is in principle exact, can suffer from divergent instabilities. The truncated Wigner function, furthermore, is able to reproduce the non-Gaussian correlations while satisfying the condition for purity., Comment: Corrected the rather obvious typos in Eqs (9)-(10). Expanded discussion on +P, sampling error and related issues. To appear in Phys. Rev. A

We investigate the effects of a squeezed pump on the quantum properties and conversion efficiency of the light produced in single-pass second harmonic generation. Using stochastic integration of the two-mode equations of motion in the positive-P representation, we find that larger violations of continuous-variable harmonic entanglement criteria are available for lesser effective interaction strengths than with a coherent pump. This enhancement of the quantum properties also applies to violations of the Reid-Drummond inequalities used to demonstrate a harmonic version of the Einstein-Podolsky-Rosen paradox. We find that the conversion efficiency is largely unchanged except for very low pump intensities and high levels of squeezing., Comment: 19 pages, 7 figures

Two Kerr-squeezed optical beams can be combined in a beamsplitter to produce non-Gaussian continuous-variable entangled states. We characterize the non-Gaussian nature of the output by calculating the third-order cumulant of quadrature variables, and predict the level of entanglement that could be generated by evaluating the Duan-Simon and Reid Einstein-Podolsky-Rosen criteria. These states have the advantage over Gaussian states and non-Gaussian measurement schemes in that the well known, efficient and proven technology of homodyne detection may be used for their characterisation. A physical demonstration maintaining the important features of the model could be realised using two optical fibres, beamsplitters, and homodyne detection., Comment: 6 pages, 7 figures

A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains well-bounded, which defines a useful simulation time. We analyse the application of the Gaussian phase-space representation to the dynamics of the dissociation of an ultra-cold molecular gas. We show how the choice of mapping to stochastic differential equations can be used to tailor the stochastic behaviour, and thus the useful simulation time. In the phase-space approach, it is only averages of stochastic trajectories that have a direct physical meaning. Whether particular constants of the motion are satisfied by individual trajectories depends on the choice of mapping, as we show in examples., Comment: Final published version; Comput. Phys. Commun. (2011)

We show that Rydberg states in an ultra-cold gas can be excited with strongly preferred nearest-neighbor distance if densities are well below saturation. The scheme makes use of an echo sequence in which the first half of a laser pulse excites Rydberg states while the second half returns atoms to the ground state, as in the experiment of Raitzsch et al. [Phys. Rev. Lett. 100 (2008) 013002]. Near to the end of the echo sequence, almost any remaining Rydberg atom is separated from its next-neighbor Rydberg atom by a distance slightly larger than the instantaneous blockade radius half-way through the pulse. These correlations lead to large deviations of the atom counting statistics from a Poissonian distribution. Our results are based on the exact quantum evolution of samples with small numbers of atoms. We finally demonstrate the utility of the omega-expansion for the approximate description of correlation dynamics through an echo sequence., Comment: 8 pages, 6 figures

We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wick's factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems., Comment: Final published version

We review and characterize the quantum coherence measures that are most useful for quantum gases, including Bose-Einstein condensates (BEC) and ultra-cold fermions, and outline how to calculate these in the typically dynamical environment of an interacting multi-mode quantum gas., Comment: short review, 12 pages

We give an outlook on the future of coherence theory and many-body quantum dynamics as experiments develop in the arena of ultra-cold atoms. Novel results on quantum heating of center-of-mass temperature in evaporative cooling and simulation methods for long-range interactions are obtained, using positive-P phase-space techniques., Comment: 16 pages; minor amendments - typos, some formatting, updated references

Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the early work of Wigner, Glauber and Sudarshan. We focus on modern phase-space approaches using non-classical phase-space representations. These lead to the Gaussian representation, which unifies bosonic and fermionic phase-space. Examples treated include quantum solitons in optical fibers, colliding Bose-Einstein condensates, and strongly correlated fermions on lattices., Comment: Short Review (10 pages); Corrected typo in eq (14); Added a few more references

We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fibre, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibres. The research represents a significant experimental test of first-principles time-domain quantum dynamics in a one-dimensional interacting Bose gas coupled to dissipative reservoirs., Comment: 4 pages, 4 figures

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus enables first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness and positivity of the basis, and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anti-commuting Grassmann variables.

We introduce a unified Gaussian quantum operator representation for fermions and bosons. The representation extends existing phase-space methods to Fermi systems as well as the important case of Fermi-Bose mixtures. It enables simulations of the dynamics and thermal equilibrium states of many-body quantum systems from first principles. As an example, we numerically calculate finite-temperature correlation functions for the Fermi Hubbard model, with no evidence of the Fermi sign problem., Comment: 4 pages, 2 figures, to appear in Comp. Phys. Comm

We summarize recent theoretical results for the signatures of strongly correlated ultra-cold fermions in optical lattices. In particular, we focus on: collective mode calculations, where a sharp decrease in collective mode frequency is predicted at the onset of the Mott metal-insulator transition; and correlation functions at finite temperature, where we employ a new exact technique that applies the stochastic gauge technique with a Gaussian operator basis., Comment: To appear, Journal of Modern Optics

We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behaviour in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas., Comment: More references and examples. Much less mathematical material

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application, we calculate finite-temperature properties of the two dimensional Hubbard model., Comment: 4 pages, 3 figures, Revised version has expanded discussion, simplified mathematical presentation, and application to 2D Hubbard model

We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are compared, as well the general question of strategies for choosing the gauge., Comment: 11 pages, 2 figures, to be published in Proceedings of the 16th International Conference on Laser Spectroscopy (ICOLS), Palm Cove, Australia (2003)

We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phase-matching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher order gain bands., Comment: 4 pages, 3 figures expanded with more explanation and mathematical detail

We consider the propagation of broad optical beams through slab waveguides with a purely quadratic nonlinearity and containing linear and nonlinear long-period quasi-phase-matching gratings. An exact Floquet analysis on the periodic, plane-wave solution shows that the periodicity can drastically alter the growth rate of the modulational instability but that it never completely removes the instability. The results are confirmed by direct numerical simulation, as well as through a simpler, approximate theory for the averaged fields that accurately predicts the low-frequency part of the spectrum., Comment: 10 Pages, 13 figures (some in two parts) new version has some typos removed and extra references and explanation added

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature., Comment: 4 pages, 7 figures corrected minor misprints

We analyze the quantum dynamics of radiation propagating in a single mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known nonlinear effects and quantum noise sources, including linear gain and loss. Both Markovian and frequency-dependent, non-Markovian reservoirs are treated. This allows quantum Langevin equations to be calculated, which have a classical form except for additional quantum noise terms. In practical calculations, it is more useful to transform to Wigner or +$P$ quasi-probability operator representations. These result in stochastic equations that can be analyzed using perturbation theory or exact numerical techniques. The results have applications to fiber optics communications, networking, and sensor technology., Comment: 1 figure

The dynamics of a soliton propagating in a single-mode optical fiber with gain, loss, and Raman coupling to thermal phonons is analyzed. Using both soliton perturbation theory and exact numerical techniques, we predict that intrinsic thermal quantum noise from the phonon reservoirs is a larger source of jitter and other perturbations than the gain-related Gordon-Haus noise, for short pulses, assuming typical fiber parameters. The size of the Raman timing jitter is evaluated for both bright and dark (topological) solitons, and is larger for bright solitons. Because Raman thermal quantum noise is a nonlinear, multiplicative noise source, these effects are stronger for the more intense pulses needed to propagate as solitons in the short-pulse regime. Thus Raman noise may place additional limitations on fiber-optical communications and networking using ultrafast (subpicosecond) pulses., Comment: 3 figures

A Bose-Einstein condensate may be used to make precise measurements of weak forces, utilizing the macroscopic occupation of a single quantum state. We present a scheme which uses a condensate in a double well potential to do this. The required initial state of the condensate is discussed, and the limitations on the sensitivity due to atom collisions and external coupling are analyzed., Comment: 12 pages, 2 figures, Eq.(41) has been corrected

We report on dynamical simulations of Bose-Einstein condensation via evaporative cooling in an atomic trap. The results show evidence for spontaneous vortex formation and quantum dynamics in small traps., Comment: 4 pages, 3 figures

We investigate a non-destructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement back-action noise alone., Comment: 8 pages, 12 figures to appear in PRA