Goldstone modes and bifurcations in phase-separated binary condensates at finite temperature

Roy, Arko; Gautam, Sandeep; Angom, D.

doi:10.1103/physreva.89.013617

Cited by 31 publications

(41 citation statements)

References 46 publications

(78 reference statements)

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“…This result has important experimental implications, and demonstrates why it is a major challenge to obtain sandwich type density profiles in TBEC experiments. The appearance of a third Goldstone mode in TBECs with sandwich type density profile at phase-separation in Rb-Na is another finding, which confirms and adds to the similar result reported in our previous work [17]. This Goldstone mode is associated with the fragmentation of the condensate species at the edges, Na in the present work, into two distinct condensates.…”

Section: Discussionsupporting

confidence: 92%

“…This breaks the z-parity symmetry of the system, and the zero-energy mode then starts to regain energy after phase-separation [15]. Detailed discussions on Goldstone modes and bifurcations in TBECs with or without soliton are discussed in our previous works [17,19].…”

Section: Third Goldstone Mode Inmentioning

confidence: 93%

“…3, 4 as elaborated in Ref. [17]. In the present study, we examine the ground state of the TBEC and compute the energy eigenmodes at zero temperature both in miscible (U 12 < √ U 11 U 22 ) and immiscible (U 12 > √ U 11 U 22 ) regimes with co-incident and non co-incident trap centers.…”

Section: Theory Of Two Component Becmentioning

confidence: 99%

“…Applying the same formalism, the ground state of a quasi-1D TBEC is described by a pair of coupled generalized GP equations [17],ĥ…”

Section: Theory Of Two Component Becmentioning

confidence: 99%

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Evolution of Goldstone mode in binary condensate mixtures

Roy

Gautam

Angom

2015

Eur. Phys. J. Spec. Top.

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Abstract. We show that the third Goldstone mode in the two-species condensate mixtures, which emerges at phase-separation, gets hardened when the confining potentials have separated trap centers. The sandwich type condensate density profiles, in this case, acquire a sideby-side density profile configuration. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution and density profiles for these phase transitions at T = 0.

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Section: Discussionsupporting

confidence: 92%

Section: Third Goldstone Mode Inmentioning

confidence: 93%

Section: Theory Of Two Component Becmentioning

confidence: 99%

“…Applying the same formalism, the ground state of a quasi-1D TBEC is described by a pair of coupled generalized GP equations [17],ĥ…”

Section: Theory Of Two Component Becmentioning

confidence: 99%

See 2 more Smart Citations

Evolution of Goldstone mode in binary condensate mixtures

Roy

Gautam

Angom

2015

Eur. Phys. J. Spec. Top.

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“…The ripple modes, or ripplons if identified as quasiparticles, emerge on a domain wall [14][15][16] (DW) of a mixture of two kinds of BECs and also possess the same dispersion relation with classical fluids in infinite-size systems 17,18 , and the analogous phenomena of the Kelvin-Helmholtz and Rayleigh-Taylor instabilities were also found [19][20][21] . There are also related issues [22][23][24] . Recently, a new insight has been brought to these gapless modes, stimulated by a renewed understanding on NambuGoldstone modes (NGMs) in non-relativistic systems [25][26][27][28][29][30] .…”

Section: Introductionmentioning

confidence: 99%

Nambu-Goldstone modes propagating along topological defects: Kelvin and ripple modes from small to large systems

2015

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Nambu-Goldstone modes associated with (topological) defects such as vortices and domain walls in (super)fluids are known to possess quadratic/non-integer dispersion relations in finite/infinite-size systems. Here, we report interpolating formulas connecting the dispersion relations in finite-and infinite-size systems for Kelvin modes along a quantum vortex and ripplons on a domain wall in superfluids. Our method can provide not only the dispersion relations but also the explicit forms of quasiparticle wavefunctions (u, v). We find a complete agreement between the analytical formulas and numerical simulations. All these formulas are derived in a fully analytical way, and hence not empirical ones. We also discuss common structures in the derivation of these formulas and speculate on the general procedure.

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FACt: FORTRAN toolbox for calculating fluctuations in atomic condensates

Roy

Pal

Gautam

et al. 2020

Computer Physics Communications

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We develop a FORTRAN code to compute fluctuations in atomic condensates (FACt) by solving the Bogoliubov-de Gennes (BdG) equations for two component Bose-Einstein condensate (TBEC) in quasi two dimensions. The BdG equations are recast as matrix equations and solved self consistently. The code is suitable for handling quantum fluctuations as well as thermal fluctuations at temperatures below the critical point of Bose-Einstein condensation. The code is versatile, and the ground state density profile and low energy excitation modes obtained from the code can be easily adapted to compute different properties of TBECs -ground state energy, overlap integral, quasi particle amplitudes of BdG spectrum, dispersion relation and structure factor and other related experimental observables.External routines/libraries: ARPACK Subprograms used: Journal reference of previous version:* Nature of problem: Compute the ground state density profile, ground state energy and chemical potential for individual species, evaluate the quasiparticle mode energies and corresponding amplitudes which can capture the transformation of the modes against the change of the parameters (intraspecies interaction, interspecies interaction, anisotropy parameter etc.) using Hartree-Fock Bogoliubov theory with the Popov approximation Calculate the overlap integral, dispersion relation and structure factor. Solution method: In the first step, the pair of coupled Gross-Pitaevskii (GP) equations are solved using split step Crank-Nicolson method to compute the condensate density.To solve BdG equations, as a basic input the first N b harmonic oscillator eigenstates are chosen as a basis to generate the BdG matrix with dimension of 4(N b + 1)(N b + 1) × 4(N b + 1)(N b + 1). Since the matrix size rapidly increases with N b , ARPACK routines are used to diagonalise the BdG matrix efficiently. To compute the fluctuation and noncondensate density, a set of the low energy quasiparticle amplitudes above a threshold value of the Bose factor are considered. The equations are then solved iteratively till the condensate, and non-condensate densities converge to predefined accuracies. To accelerate the convergence we use the method of successive under-relaxation (SUR).Restrictions: For a large system size, if the harmonic oscillator basis size is also taken to be large, the dimension of the BDG matrix becomes huge. It may take several days to compute the low energy modes at finite temperature and this package may be computationally expensive.Additional comments:After successful computation of this package, one should obtain the equilibrium density profiles for TBEC, low energy Bogoliubov modes and the corresponding quasiparticle amplitudes. In addition, one can calculate the dispersion relation, structure factor, overlap integral, correlation function, etc. using this package with minimal modifications. In the theory section of the manuscript, we have provided the expressions to compute the above quantities numerically.Running time: ∼ 10 minutes for the sample case. For ...

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Goldstone modes and bifurcations in phase-separated binary condensates at finite temperature

Cited by 31 publications

References 46 publications

Evolution of Goldstone mode in binary condensate mixtures

Evolution of Goldstone mode in binary condensate mixtures

Nambu-Goldstone modes propagating along topological defects: Kelvin and ripple modes from small to large systems

FACt: FORTRAN toolbox for calculating fluctuations in atomic condensates

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