Equilibrium ground state of 133 Cs-87 Rb TBEC at zero temperature for three different values of interspecies interaction strength (a) a CsRb = 100a 0 : TBEC is in miscible domain (b) a CsRb = 200a 0 : TBEC is in shell structures domain and (c) a CsRb = 220a 0 : TBEC is side by side phase separated. nc is measured in units of a −2 osc and the spatial coordinates x is measured in units of aosc. 

Contexts in source publication

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...

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... this section we describe the zero temperature condensate density profiles n ic and the Bogoliubov quasi particle amplitudes u and v in miscible and immiscible regions. In Fig.1, we show the density of condensate atoms n ic (x, 0). This figure is obtained by plotting column 1, 3 and 5 of file den00x.dat for three different inter species interaction strengths. If otherwise mentioned, in all the figures the species 1 and 2 correspond to 133 Cs and 87 Rb, respectively. For Fig.1(a) and Fig.1(c) we consider total 2000 of atoms where as in Fig.1(b) we consider total 5000 atoms. To obtain equilibrium ground states and avoid metastable states for side by side phase separated TBEC, it is essential to start the iterations with the initial guess wave functions having spatially separated peaks. This is implemented in the subroutine initialize.f90 by setting SHIFT1 = 5.0D0. This also ensures rapid convergence. For other density configurations, SHIFT1 = 0.0D0 is considered and implies complete overlap of the initial guess wave functions. From Fig.1(b) it is clear that the TBEC shell structured for the chosen set of pa- rameters, where 133 Cs BEC is at the core and with the 87 Rb BEC surrounding it. In Fig.1(c), 133 Cs and 87 Rb BECs occupy right and left sides, respectively. Here, the po- sitions of the BECs are not unique, and can interchange depending on the shift in initial guess wave functions. Below we provide content of the input file to corresponding to Fig.1(a). input file corresponding to Fig.1 The formation of BEC is associated with the spontaneous symmetry breaking (SSB) of U (1) global gauge. Due to this SSB, in trapped quasi-2D TBEC, the low-energy BdG spectrum has two Goldstone modes for each of the condensate species. In other words, the excitation spectrum of the BEC is gapless, and the two lowest energy modes with finite energies are the dipole modes. The dipole modes which oscillate out-of- phase with each other are called slosh modes. The in-phase slosh modes with center- of-mass motion are called the Kohn modes and have frequency identical to the natural frequency of the harmonic confining potential. Thus the frequency of the Kohn mode is independent of the type of interactions and interaction strength as well. For this reason the getting Kohn mode energy close to 1 serves as an important consistency check of our FACt ...