arXiv subjects

Peter D. Drummond

Publications and source records attributed to Peter D. Drummond.

72 records · Page 4Linked to original sources

arXiv2008

Hybrid phase-space simulation method for interacting Bose fields

We introduce an approximate phase-space technique to simulate the quantum dynamics of interacting bosons. With the future goal of treating Bose-Einstein condensate systems, the method is designed for systems with a natural separation into highly occupied (condensed) modes and lightly occupied modes. The method self-consistently uses the Wigner representation to treat highly occupied modes and the positive-P representation for lightly occupied modes. In this method, truncation of higher-derivative terms from the Fokker-Planck equation is usually necessary. However, at least in the cases investigated here, the resulting systematic error, over a finite time, vanishes in the limit of large Wigner occupation numbers. We tested the method on a system of two interacting anharmonic oscillators, with high and low occupations, respectively. The Hybrid method successfully predicted atomic quadratures to a useful simulation time 60 times longer than that of the positive-P method. The truncated Wigner method also performed well in this test. For the prediction of the correlation in a quantum nondemolition measurement scheme, for this same system, the Hybrid method gave excellent agreement with the exact result, while the truncated Wigner method showed a large systematic error.

quant-ph↗

arXiv2008

Multi-component strongly attractive Fermi gas: a color superconductor in a one-dimensional harmonic trap

Recent advances in ultra-cold atomic Fermi gases make it possible to achieve a fermionic superfluid with multiple spin components. In this context, any mean-field description is expected to fail, owing to the presence of tightly bound clusters or molecules that consist of more than two particles. Here we present a detailed study of a strongly interacting multi-component Fermi gas in a highly elongated or quasi-one-dimensional harmonic trap, which could be readily obtained in experiment. By using the exact Bethe ansatz solution and a local density approximation treatment of the harmonic trap, we investigate the equation of state of the multi-component Fermi gas in both a homogeneous and trapped environment, as well as the density profiles and low-energy collective modes. The binding energy of multi-component bound clusters is also given. We show that there is a peak in the collective mode frequency at the critical density for a deconfining transition to a many-body state that is analogous to the quark color superconductor state expected in neutron stars.

cond-mat.supr-con↗

arXiv2007

Fulde-Ferrell-Larkin-Ovchinnikov states in one-dimensional spin-polarized ultracold atomic Fermi gases

We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov-de Gennes equations, as well as the exact soluble Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired BCS state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimension. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure is shown up, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.

cond-mat.stat-mech↗

arXiv2007

Raman-induced limits to efficient squeezing in optical fibers

We report new experiments on polarization squeezing using ultrashort photonic pulses in a single pass of a birefringent fiber. We measure what is to our knowledge a record squeezing of -6.8 +/- 0.3 dB in optical fibers which when corrected for linear losses is -10.4 +/- 0.8 dB. The measured polarization squeezing as a function of optical pulse energy, which spans a wide range from 3.5-178.8 pJ, shows a very good agreement with the quantum simulations and for the first time we see the experimental proof that Raman effects limit and reduce squeezing at high pulse energy.

quant-ph↗

arXiv2007

Universal thermodynamics of strongly interacting Fermi gases

Strongly interacting Fermi gases are of great current interest. Not only are fermions the most common particles in the universe, but they are also thought to have a universal thermodynamic behavior for strong interactions \cite{heiselberg,carlson,ho}. Recent experiments on ultra-cold Fermi gases provide an unprecedented opportunity to test universality in the laboratory \cite{hara,thomas,partridge,stewart,luo}. In principle this allows - for example - the interior properties of hot, dense neutron stars to be investigated on earth. Here we carry out a detailed test of this prediction. We analyze results from three ultra-cold fermion experiments involving two completely distinct atomic species in different kinds of atomic trap environments \cite{partridge,stewart,luo}. The data is compared with the predictions of a recent strong interaction theory \cite{hldepl,hldpra}. Excellent agreement is obtained, with no adjustable parameters. By extrapolating to zero temperature, we show that the experimental measurements yield a many-body parameter} $\mathbf{β\simeq-0.59\pm.07}$, \textbf{describing the universal energy of strongly interacting Fermi gases.

cond-mat.str-el↗

arXiv2007

Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz

The exactly solvable Lieb-Liniger model of interacting bosons in one-dimension has attracted renewed interest as current experiments with ultra-cold atoms begin to probe this regime. Here we numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss the novel features of the solutions, and how they deviate from the well-known string solutions [H. B. Thacker, Rev. Mod. Phys.\ \textbf{53}, 253 (1981)] at finite densities. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Finally we compare our results to those of exact diagonalization of the many-body Hamiltonian in a truncated basis. We also present excited state solutions and the excitation spectrum for the repulsive 1D Bose gas on a ring.

cond-mat.other↗

arXiv2007

Mean field thermodynamics of a spin-polarized spherically trapped Fermi gas at unitarity

We calculate the mean-field thermodynamics of a spherically trapped Fermi gas with unequal spin populations in the unitarity limit, comparing results from the Bogoliubov-de Gennes equations and the local density approximation. We follow the usual mean-field decoupling in deriving the Bogoliubov-de Gennes equations and set up an efficient and accurate method for solving these equations. In the local density approximation we consider locally homogeneous solutions, with a slowly varying order parameter. With a large particle number these two approximation schemes give rise to essentially the same results for various thermodynamic quantities, including the density profiles. This excellent agreement strongly indicates that the small oscillation of order parameters near the edge of trap, sometimes interpreted as spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states in previous studies of Bogoliubov-de Gennes equations, is a finite size effect. We find that a bimodal structure emerges in the density profile of the minority spin state at finite temperature, as observed in experiments. The superfluid transition temperature as a function of the population imbalance is determined, and is shown to be consistent with recent experimental measurements. The temperature dependence of the equation of state is discussed.

cond-mat.str-el↗

arXiv2007

Visualization of vortex bound states in polarized Fermi gases at unitarity

We analyse theoretically a single vortex in 3D trapped atomic Fermi gases with population polarization near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied for the majority component. As a result, the local density difference at the core center acquires a sudden rise at low temperautres. This provides a visualization of the lowest bound state within the absorption imaging technique. As the polarization increases, the core expands gradually, and correspondingly, the energy of the lowest bound state decreases.

cond-mat.supr-con↗

arXiv2007

Phase diagram of a strongly interacting polarized Fermi gas in one dimension

Based on the integrable Gaudin model and local density approximation, we discuss the phase structure of one-dimensional trapped Fermi gases with imbalanced spin populations for arbitrary attractive interactions. A phase separation state, with a polarized superfluid core immersed in an unpolarized superfluid shell, emerges below a critical spin polarization. Above it, a coexistence of polarized superfluid matter and a fully polarized normal gas is favored. These two exotic states could be realized experimentally in highly elongated atomic traps, and diagnosed by measuring the lowest density compressional mode. We identify the polarized superfluid as having an FFLO structure, and predict the resulting mode frequency as a function of the spin polarization.

cond-mat.supr-con↗

arXiv2006

Equation of state of a superfluid Fermi gas in the BCS-BEC crossover

We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozieres and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available.

cond-mat.supr-con↗

arXiv2006

Temperature of a trapped unitary Fermi gas at finite entropy

We present theoretical predictions for the equation of state of a harmonically-trapped Fermi gas in the unitary limit. Our calculations rest on a study of the equation of state of a uniform gas using three distinct perturbation schemes, compared to Monte-Carlo results. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conversion into the weakly-interacting limit of molecular BEC. We predict the entropy dependence of the equation of state.

cond-mat.supr-con↗

arXiv2005

Monte Carlo techniques for real-time quantum dynamics

The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the "weight", and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The method is applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.

quant-ph↗

arXiv2005

Universality of quantum critical dynamics in a planar OPO

We analyze the critical quantum fluctuations in a coherently driven planar optical parametric oscillator. We show that the presence of transverse modes combined with quantum fluctuations changes the behavior of the `quantum image' critical point. This zero-temperature non-equilibrium quantum system has the same universality class as a finite-temperature magnetic Lifshitz transition.

quant-ph↗

arXiv2005

Signature of Mott-insulator transition with ultra-cold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultra-cold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

cond-mat.stat-mech↗

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↗

arXiv2003

Gaussian quantum operator representation for bosons

We introduce the Gaussian quantum operator representation, using the most general multi-mode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems, and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.

quant-ph↗

arXiv2000

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the in and out creation and annihilation operators is found which allows one to calculate the S-matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum noise terms are required.

quant-ph↗

arXiv2000

How to mode-lock an atom laser

We consider a possible technique for mode-locking an atom laser, based on the generation of a dark soliton in a ring-shaped Bose-Einstein condensate, with repulsive atomic interactions. The soliton is a kink, with angular momentum per particle equal to \hbar/2. It emerges naturally, when the condensate is stirred at the soliton velocity, and subsequently outcoupled with a periodic Raman pulse-train. The result is a replicating coherent field inside the atom laser. We give a numerical demonstration of the generation and stabilization of the soliton.

cond-mat↗