Since the discovery of superfluidity in 4He and Landau's phenomenological theory, the relationship between Bose condensation and superfluidity has been intensely debated. 4He is known by now to be both superfluid and condensed at low temperature, and more generally, in dimension D≥2, all superfluid bosonic models realized in experiments are condensed in their ground state, the most recent example being provided by ultracold bosonic atoms trapped in an optical lattice. In this Letter, it is shown that a 2D gas of bosons which is not condensed at T=0 can be achieved by populating a layer through a frustrated proximity effect from a superfluid reservoir. This condensate-free bosonic fluid is further shown to be a superfluid with incommensurate correlations.Since the discovery of superfluidity in 4He and Landau's phenomenological theory, the relationship between Bose condensation and superfluidity has been intensely debated. 4He is known by now to be both superfluid and condensed at low temperature, and more generally, in dimension D≥2, all superfluid bosonic models realized in experiments are condensed in their ground state, the most recent example being provided by ultracold bosonic atoms trapped in an optical lattice. In this Letter, it is shown that a 2D gas of bosons which is not condensed at T=0 can be achieved by populating a layer through a frustrated proximity effect from a superfluid reservoir. This condensate-free bosonic fluid is further shown to be a superfluid with incommensurate correlations.

arXiv:1009.5978Physical Review LettersJul 11, 201111 citations

Bose–Einstein condensation and superfluidity

Bipin R. Desai

Cambridge University Press eBooksDec 3, 200945 citations

Bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high- $T_c$ cuprates and other systemsBosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-$T_c$ cuprates and other systems

Safarali Dzhumanov

The criteria for bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high- $T_c$ cuprates and other pseudogap matters are formulated by using the uncertainty principle and the boson mean field theory. We argue that the BCS-type s- or d-wave superconductivity occurring in the fermionic limit of Cooper pairs (which exist in ordinary metals and heavily overdoped cuprates with large Fermi energies) is not characteristic of underdoped to overdoped cuprates with low Fermi energies. The superconducting order parameter in high- $T_c$ cuprates and other pseudogap matters cannot be determined as the BCS-like (s- or d-wave) gap. We show that the unconventional superconductivity/superfluidity occurring in the bosonic limit of Cooper pairs exists in low Fermi energy systems where the bosonic Cooper pairs are formed at a pseudogap temperature T* above the uperconducting/superfluid transition temperature $T_c$ and then such bosons condenses into a Bose superfluid at $T_c$ . The pair condensation of attracting bosons occurs at $T_c$ and then their single particle condensation sets in at $T_c^*$ lower than $T_c$ (in three dimensions (3D)) or at T=0 (in two dimensions (2D)). The coherent single particle and pair condensates of bosons exist as two distinct superfluid phases below $T_c$ . By solving the mean field equations for high- $T_c$ cuprates, the novel superconducting states (i.e., a vortex-like state existing below the temperature $T_v=T^{2D}_c$ lower than T* but higher than $T_c=T^{3D}_c$ and two superconducting phases below $T_c$ ) and their properties characterized by the boson superfluid stiffness are determined and compared with the key experimental findings. The novel Bose-liquid superconductivity and superfluidity exists also in other exotic superconductors/superfluids, including quantum liquids, atomic Fermi gases and low-density nuclear matter.The criteria for bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-$T_c$ cuprates and other pseudogap matters are formulated by using the uncertainty principle and the boson mean field theory. We argue that the BCS-type s- or d-wave superconductivity occurring in the fermionic limit of Cooper pairs (which exist in ordinary metals and heavily overdoped cuprates with large Fermi energies) is not characteristic of underdoped to overdoped cuprates with low Fermi energies. The superconducting order parameter in high-$T_c$ cuprates and other pseudogap matters cannot be determined as the BCS-like (s- or d-wave) gap. We show that the unconventional superconductivity/superfluidity occurring in the bosonic limit of Cooper pairs exists in low Fermi energy systems where the bosonic Cooper pairs are formed at a pseudogap temperature T* above the uperconducting/superfluid transition temperature $T_c$ and then such bosons condenses into a Bose superfluid at $T_c$. The pair condensation of attracting bosons occurs at $T_c$ and then their single particle condensation sets in at $T_c^*$ lower than $T_c$ (in three dimensions (3D)) or at T=0 (in two dimensions (2D)). The coherent single particle and pair condensates of bosons exist as two distinct superfluid phases below $T_c$. By solving the mean field equations for high-$T_c$ cuprates, the novel superconducting states (i.e., a vortex-like state existing below the temperature $T_v=T^{2D}_c$ lower than T* but higher than $T_c=T^{3D}_c$ and two superconducting phases below $T_c$) and their properties characterized by the boson superfluid stiffness are determined and compared with the key experimental findings. The novel Bose-liquid superconductivity and superfluidity exists also in other exotic superconductors/superfluids, including quantum liquids, atomic Fermi gases and low-density nuclear matter.

arXiv:1709.02110Sep 7, 20170 citations

Superfluidity and Bose-Einstein condensation in optical lattices and porous media: A path integral Monte Carlo study

Ali A. Shams, H. R. Glyde

We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate (1) the impact of the periodic external potential on the spatial distribution of the condensate, and (2) the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells (tight binding) and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate (1) the impact of the periodic external potential on the spatial distribution of the condensate, and (2) the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells (tight binding) and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.

Physical Review BJun 8, 20099 citations

Bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-

T_c

cuprates and other systems

The criteria for bosonization of Cooper pairs and novel Bose-liquid superconductivity and superfluidity in high-

T_c

cuprates and other pseudogap matters are formulated by using the uncertainty principle and the boson mean field theory. We argue that the BCS-type s- or d-wave superconductivity occurring in the fermionic limit of Cooper pairs (which exist in ordinary metals and heavily overdoped cuprates with large Fermi energies) is not characteristic of underdoped to overdoped cuprates with low Fermi energies. The superconducting order parameter in high-

T_c

cuprates and other pseudogap matters cannot be determined as the BCS-like (s- or d-wave) gap. We show that the unconventional superconductivity/superfluidity occurring in the bosonic limit of Cooper pairs exists in low Fermi energy systems where the bosonic Cooper pairs are formed at a pseudogap temperature T* above the uperconducting/superfluid transition temperature

T_c

and then such bosons condenses into a Bose superfluid at

T_c

. The pair condensation of attracting bosons occurs at

T_c

and then their single particle condensation sets in at

T_c^*

lower than

T_c

(in three dimensions (3D)) or at T=0 (in two dimensions (2D)). The coherent single particle and pair condensates of bosons exist as two distinct superfluid phases below

T_c

. By solving the mean field equations for high-

T_c

cuprates, the novel superconducting states (i.e., a vortex-like state existing below the temperature

T_v=T^{2D}_c

lower than T* but higher than

T_c=T^{3D}_c

and two superconducting phases below

T_c

) and their properties characterized by the boson superfluid stiffness are determined and compared with the key experimental findings. The novel Bose-liquid superconductivity and superfluidity exists also in other exotic superconductors/superfluids, including quantum liquids, atomic Fermi gases and low-density nuclear matter.