... J. Brand@ massey. ac. nz Lincoln D. Carr Colorado School of Mines, Golden CO 80401, USA. lcar... more ... J. Brand@ massey. ac. nz Lincoln D. Carr Colorado School of Mines, Golden CO 80401, USA. lcarr@ mines. edu Ricardo Carretero-Gonzalez San Diego State University, San Diego CA, 92182-7720, USA. carreter@ sciences. sdsu. ...
A general theory of extended two-particle Green's functions constructed from orthonormal ... more A general theory of extended two-particle Green's functions constructed from orthonormal extended states is presented. Three types of fermionic propagators are considered that allow the description of a wide range of two-particle processes in non-relativistic many-body systems: the extended particle-hole, particle-particle, and hole-hole Green's functions. Each member of the considered class of two-particle propagators fulfils a Dyson equation and defines
A relation between the number of bound collective excitations of an atomic Bose-Einstein condensa... more A relation between the number of bound collective excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalises Levinson's theorem. Specific features of the Bogoliubov model such as complex-energy and continuum bound states are discussed and a numerical example is given.
By creating superpositions in a Hilbert space consisting of many modes, rather than just two, pha... more By creating superpositions in a Hilbert space consisting of many modes, rather than just two, phase shifts can be measured with Heisenberg limited precision and have similar robustness to particle loss as unentangled states. Previous proposals for measuring phase shifts with Heisenberg limited precision require a two-mode highly entangled state, for example a NOON state. Unfortunately these states rapidly lose
Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and num... more Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and number of depleted particles completely determines the dynamics of dark solitons on a slowlyvarying background density. For the unitary Fermi gas we determine these relations from general scaling arguments and conservation of local particle number. We find solitons to oscillate sinusoidally at the trap frequency reduced by a factor of 1/ √ 3. Numerical integration of the time-dependent Bogoliubov-de Gennes equation determines spatial profiles and soliton dispersion relations across the BEC-BCS crossover and proves consistent with the scaling relations at unitarity.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2004
A time-dependent Kohn-Sham scheme for 1D bosons with contact interaction is derived based on a mo... more A time-dependent Kohn-Sham scheme for 1D bosons with contact interaction is derived based on a model of spinor fermions. This model is specifically designed for the study of the strong interaction regime close to the Tonks gas. It allows us to treat the transition from the strongly interacting Tonks-Girardeau to the weakly interacting quasicondensate regime and provides an intuitive picture of the extent of fermionization in the system. An adiabatic localdensity approximation is devised for the study of time-dependent processes. This scheme is shown to yield not only accurate ground-state properties but also overall features of the elementary excitation spectrum, which is described exactly in the Tonks-gas limit. S288 J Brand a Fermi system can be extended to arbitrary interaction strength at the expense of a highly singular interaction in the fermionic picture. For the homogeneous Bose gas, exact solutions for stationary states at arbitrary interaction strength can be found using the Bethe ansatz . Although the exact solutions show a continuous transition between the perturbative regime of weakly interacting bosons and the strongly correlated, fermionized regime, they do not prove very useful for the study of time-dependent processes or inhomogeneous situations. Neither do they provide us with a simple, intuitive picture of how strong the degree of fermionization is in a given system. The crossover from the quasicondensate to the fermionized Tonks gas has also been studied in Inspired by the works of Haldane [13], Sutherland and others on the concept of exclusion statistics describing a crossover between fermionic and bosonic statistics in 1D systems, we study a model which explicitly allows this transition and provides an intuitive picture of the degree of fermionization. In order to devise a practical scheme for treating time-dependent and inhomogeneous systems we employ DFT and develop a time-dependent Kohn-Sham formalism based on the auxiliary model system of N non-interacting spin-(ν−1)/2 fermions. This model is chosen because the spin degeneracy may simulate the level attraction or the bunching of single-particle quasi momenta in the interacting bosonic system . The interaction energy of the Bose system is simulated by the kinetic energy of the spin-degenerate fermions. In this work we will study the model in the simplest and most generic approximation: the adiabatic local-density approximation (ALDA). The limiting case of infinite interaction strength is obtained easily and is treated exactly with ν = 1. The opposite limit of weak interaction can also be treated accurately within the proposed formalism with ν = N where the perturbative Gross-Pitaevskii and Bogoliubov equations are recovered asymptotically. In the general case of arbitrary interaction strength, the spin degeneracy ν is fixed by requiring the correct low-energy asymptotics of the excitation spectrum, which is analysed in the framework of linear-response theory. The resulting model is suitable for the study of time-dependent processes in inhomogeneous 1D Bose gases close to the Tonks-gas limit. The properties of this approximate model are analysed and systematic improvements are suggested.
We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with eq... more We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with equal density. The interplay of the isotropic s-wave interaction and anisotropic long-range dipolar interaction reveals rich physics. We find that the single-particle momentum distribution has a characteristic ellipsoidal shape that can be reasonably represented by a deformation parameter α defined similarly to the normal phase. Interesting momentum-dependent features of the order parameter are identified. We calculate the critical temperatures of both the singlet and triplet superfluid, suggesting a possible pairing symmetry transition by tuning the s-wave or dipolar interaction strength.
Journal of Physics A: Mathematical and General, 2005
We study the scattering properties of topological solitons on obstructions in the form of holes a... more We study the scattering properties of topological solitons on obstructions in the form of holes and barriers. We use the 'new baby Skyrme' model in (2+1) dimensions and we model the obstructions by making the coefficient of the baby skyrme model potential -position dependent. We find that that the barrier leads to the repulsion of the solitons (for low velocities) or their complete transmission (at higher velocities) with the process being essentially elastic. The hole case is different; for small velocities the solitons are trapped while at higher velocities they are transmitted with a loss of energy. We present some comments explaining the observed behaviour.
We revisit recent claims about the instability of non-rotating tunnel coupled annular Bose-Einste... more We revisit recent claims about the instability of non-rotating tunnel coupled annular Bose-Einstein condensates leading to the emergence of angular-momentum Josephson oscillation [Phys. Rev. Lett. 98, 050401 (2007)]. It was predicted that all stationary states with uniform density become unstable in certain parameter regimes. By careful analysis, we arrive at a different conclusion. We show that there is a stable non-rotating and uniform ground state for any value of the tunnel coupling and repulsive interactions. The instability of an excited state with π phase difference between the condensates can be interpreted in terms of the familiar snake instability. We further discuss the sign of the tunnel coupling through a separating barrier, which carries significance for the nature of the stationary states. It is found to always be negative for physical reasons.
We present numerical calculations of the snake instability in a Fermi superfluid within the Bogol... more We present numerical calculations of the snake instability in a Fermi superfluid within the Bogoliubov-de Gennes theory of the BEC to BCS crossover using the random phase approximation complemented by time-dependent simulations. We examine the snaking behaviour across the crossover and quantify the timescale and lengthscale of the instability. While the dynamic shows extensive snaking before eventually producing vortices and sound on the BEC side of the crossover, the snaking dynamics is preempted by decay into sound due to pair breaking in the deep BCS regime. At the unitarity limit, hydrodynamic arguments allow us to link the rate of snaking to the experimentally observable ratio of inertial to physical mass of the soliton. In this limit we witness an unresolved discrepancy between our numerical estimates for the critical wavenumber of suppression of the snake instability and recent experimental observations with an ultra-cold Fermi gas.
ABSTRACT We propose a simple stirring experiment to generate quantized ringcurrents and solitons ... more ABSTRACT We propose a simple stirring experiment to generate quantized ringcurrents and solitons in Bose-Einstein condensates in a toroidal trap geometry. Simulations of the 3D Gross-Pitaevskii equation show that pure ringcurrents can be generated efficiently by adiabatic manipulation of the condensate, which can be realized on experimental time scales. While solitons can be generated in thin tori, we show the even more robust generation of hybrid, solitary-wave-like vortices (s'vortices) in a regime of intermediate confinement. S'vortices are vortices confined to essentially one-dimensional dynamics and created by the curvature of the torus. Marking the transition between solitons and vortices, s'vortices show peculiar stability and collisional properties: In contrast to solitons, they have internal degrees of freedom and can undergo inelastic collisions. PACS: 03.75.Fi, 05.45.Yv, 67.40.Vs
ABSTRACT The Bloch dynamics of degenerate cold atoms in optical lattices is a paradigmatic proble... more ABSTRACT The Bloch dynamics of degenerate cold atoms in optical lattices is a paradigmatic problem of quantum transport theory, arid under virtually perfect experimental control. If a Bose-Einstein condensate (BEC) is loaded into truly 1D lattices, and for sufficiently small filling factors, the problem can be treated within the Bose-Hubbard model. The nonlinearity can stabilise the BEC against dispersion whilst moving across the lattice, giving rise to soliton-like solutions
... J. Brand@ massey. ac. nz Lincoln D. Carr Colorado School of Mines, Golden CO 80401, USA. lcar... more ... J. Brand@ massey. ac. nz Lincoln D. Carr Colorado School of Mines, Golden CO 80401, USA. lcarr@ mines. edu Ricardo Carretero-Gonzalez San Diego State University, San Diego CA, 92182-7720, USA. carreter@ sciences. sdsu. ...
A general theory of extended two-particle Green's functions constructed from orthonormal ... more A general theory of extended two-particle Green's functions constructed from orthonormal extended states is presented. Three types of fermionic propagators are considered that allow the description of a wide range of two-particle processes in non-relativistic many-body systems: the extended particle-hole, particle-particle, and hole-hole Green's functions. Each member of the considered class of two-particle propagators fulfils a Dyson equation and defines
A relation between the number of bound collective excitations of an atomic Bose-Einstein condensa... more A relation between the number of bound collective excitations of an atomic Bose-Einstein condensate and the phase shift of elastically scattered atoms is derived. Within the Bogoliubov model of a weakly interacting Bose gas this relation is exact and generalises Levinson's theorem. Specific features of the Bogoliubov model such as complex-energy and continuum bound states are discussed and a numerical example is given.
By creating superpositions in a Hilbert space consisting of many modes, rather than just two, pha... more By creating superpositions in a Hilbert space consisting of many modes, rather than just two, phase shifts can be measured with Heisenberg limited precision and have similar robustness to particle loss as unentangled states. Previous proposals for measuring phase shifts with Heisenberg limited precision require a two-mode highly entangled state, for example a NOON state. Unfortunately these states rapidly lose
Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and num... more Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and number of depleted particles completely determines the dynamics of dark solitons on a slowlyvarying background density. For the unitary Fermi gas we determine these relations from general scaling arguments and conservation of local particle number. We find solitons to oscillate sinusoidally at the trap frequency reduced by a factor of 1/ √ 3. Numerical integration of the time-dependent Bogoliubov-de Gennes equation determines spatial profiles and soliton dispersion relations across the BEC-BCS crossover and proves consistent with the scaling relations at unitarity.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2004
A time-dependent Kohn-Sham scheme for 1D bosons with contact interaction is derived based on a mo... more A time-dependent Kohn-Sham scheme for 1D bosons with contact interaction is derived based on a model of spinor fermions. This model is specifically designed for the study of the strong interaction regime close to the Tonks gas. It allows us to treat the transition from the strongly interacting Tonks-Girardeau to the weakly interacting quasicondensate regime and provides an intuitive picture of the extent of fermionization in the system. An adiabatic localdensity approximation is devised for the study of time-dependent processes. This scheme is shown to yield not only accurate ground-state properties but also overall features of the elementary excitation spectrum, which is described exactly in the Tonks-gas limit. S288 J Brand a Fermi system can be extended to arbitrary interaction strength at the expense of a highly singular interaction in the fermionic picture. For the homogeneous Bose gas, exact solutions for stationary states at arbitrary interaction strength can be found using the Bethe ansatz . Although the exact solutions show a continuous transition between the perturbative regime of weakly interacting bosons and the strongly correlated, fermionized regime, they do not prove very useful for the study of time-dependent processes or inhomogeneous situations. Neither do they provide us with a simple, intuitive picture of how strong the degree of fermionization is in a given system. The crossover from the quasicondensate to the fermionized Tonks gas has also been studied in Inspired by the works of Haldane [13], Sutherland and others on the concept of exclusion statistics describing a crossover between fermionic and bosonic statistics in 1D systems, we study a model which explicitly allows this transition and provides an intuitive picture of the degree of fermionization. In order to devise a practical scheme for treating time-dependent and inhomogeneous systems we employ DFT and develop a time-dependent Kohn-Sham formalism based on the auxiliary model system of N non-interacting spin-(ν−1)/2 fermions. This model is chosen because the spin degeneracy may simulate the level attraction or the bunching of single-particle quasi momenta in the interacting bosonic system . The interaction energy of the Bose system is simulated by the kinetic energy of the spin-degenerate fermions. In this work we will study the model in the simplest and most generic approximation: the adiabatic local-density approximation (ALDA). The limiting case of infinite interaction strength is obtained easily and is treated exactly with ν = 1. The opposite limit of weak interaction can also be treated accurately within the proposed formalism with ν = N where the perturbative Gross-Pitaevskii and Bogoliubov equations are recovered asymptotically. In the general case of arbitrary interaction strength, the spin degeneracy ν is fixed by requiring the correct low-energy asymptotics of the excitation spectrum, which is analysed in the framework of linear-response theory. The resulting model is suitable for the study of time-dependent processes in inhomogeneous 1D Bose gases close to the Tonks-gas limit. The properties of this approximate model are analysed and systematic improvements are suggested.
We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with eq... more We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with equal density. The interplay of the isotropic s-wave interaction and anisotropic long-range dipolar interaction reveals rich physics. We find that the single-particle momentum distribution has a characteristic ellipsoidal shape that can be reasonably represented by a deformation parameter α defined similarly to the normal phase. Interesting momentum-dependent features of the order parameter are identified. We calculate the critical temperatures of both the singlet and triplet superfluid, suggesting a possible pairing symmetry transition by tuning the s-wave or dipolar interaction strength.
Journal of Physics A: Mathematical and General, 2005
We study the scattering properties of topological solitons on obstructions in the form of holes a... more We study the scattering properties of topological solitons on obstructions in the form of holes and barriers. We use the 'new baby Skyrme' model in (2+1) dimensions and we model the obstructions by making the coefficient of the baby skyrme model potential -position dependent. We find that that the barrier leads to the repulsion of the solitons (for low velocities) or their complete transmission (at higher velocities) with the process being essentially elastic. The hole case is different; for small velocities the solitons are trapped while at higher velocities they are transmitted with a loss of energy. We present some comments explaining the observed behaviour.
We revisit recent claims about the instability of non-rotating tunnel coupled annular Bose-Einste... more We revisit recent claims about the instability of non-rotating tunnel coupled annular Bose-Einstein condensates leading to the emergence of angular-momentum Josephson oscillation [Phys. Rev. Lett. 98, 050401 (2007)]. It was predicted that all stationary states with uniform density become unstable in certain parameter regimes. By careful analysis, we arrive at a different conclusion. We show that there is a stable non-rotating and uniform ground state for any value of the tunnel coupling and repulsive interactions. The instability of an excited state with π phase difference between the condensates can be interpreted in terms of the familiar snake instability. We further discuss the sign of the tunnel coupling through a separating barrier, which carries significance for the nature of the stationary states. It is found to always be negative for physical reasons.
We present numerical calculations of the snake instability in a Fermi superfluid within the Bogol... more We present numerical calculations of the snake instability in a Fermi superfluid within the Bogoliubov-de Gennes theory of the BEC to BCS crossover using the random phase approximation complemented by time-dependent simulations. We examine the snaking behaviour across the crossover and quantify the timescale and lengthscale of the instability. While the dynamic shows extensive snaking before eventually producing vortices and sound on the BEC side of the crossover, the snaking dynamics is preempted by decay into sound due to pair breaking in the deep BCS regime. At the unitarity limit, hydrodynamic arguments allow us to link the rate of snaking to the experimentally observable ratio of inertial to physical mass of the soliton. In this limit we witness an unresolved discrepancy between our numerical estimates for the critical wavenumber of suppression of the snake instability and recent experimental observations with an ultra-cold Fermi gas.
ABSTRACT We propose a simple stirring experiment to generate quantized ringcurrents and solitons ... more ABSTRACT We propose a simple stirring experiment to generate quantized ringcurrents and solitons in Bose-Einstein condensates in a toroidal trap geometry. Simulations of the 3D Gross-Pitaevskii equation show that pure ringcurrents can be generated efficiently by adiabatic manipulation of the condensate, which can be realized on experimental time scales. While solitons can be generated in thin tori, we show the even more robust generation of hybrid, solitary-wave-like vortices (s'vortices) in a regime of intermediate confinement. S'vortices are vortices confined to essentially one-dimensional dynamics and created by the curvature of the torus. Marking the transition between solitons and vortices, s'vortices show peculiar stability and collisional properties: In contrast to solitons, they have internal degrees of freedom and can undergo inelastic collisions. PACS: 03.75.Fi, 05.45.Yv, 67.40.Vs
ABSTRACT The Bloch dynamics of degenerate cold atoms in optical lattices is a paradigmatic proble... more ABSTRACT The Bloch dynamics of degenerate cold atoms in optical lattices is a paradigmatic problem of quantum transport theory, arid under virtually perfect experimental control. If a Bose-Einstein condensate (BEC) is loaded into truly 1D lattices, and for sufficiently small filling factors, the problem can be treated within the Bose-Hubbard model. The nonlinearity can stabilise the BEC against dispersion whilst moving across the lattice, giving rise to soliton-like solutions
We theoretically study homogeneously trapped atomic Bose-Einstein condensates where all three mom... more We theoretically study homogeneously trapped atomic Bose-Einstein condensates where all three momentum components couple to a pseudo-spin-1/2 degree of freedom. Tuning the anisotropies of spin-orbit coupling and the spin-dependent interactions is shown to provide access to a rich phase diagram with a tetracritical point, first-order phase transitions, and multiple metastable phases of stripe and plane-wave character. The elementary excitation spectrum of the axial plane-wave phase features an anisotropic roton feature and can be used to probe the phase diagram. In addition to providing a versatile laboratory for studying fundamental concepts in statistical physics, the emergence of metastable phases creates new opportunities for observing false-vacuum decay and bubble nucleation in ultra-cold-atom experiments.
We consider the motion of a pointlike impurity through a three-dimensional two-component Bose-Ein... more We consider the motion of a pointlike impurity through a three-dimensional two-component Bose-Einstein condensate subject to Weyl spin-orbit coupling. Using linear-response theory, we calculate the drag force felt by the impurity and the associated anisotropic critical velocity from the spectrum of elementary excitations. The drag force is shown to be generally not collinear with the velocity of the impurity. This unusual behavior is a consequence of condensation into a finite-momentum state due to the spin-orbit coupling.
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Papers by Joachim Brand