Participants in this FAPESP thematic project:

Sadhan Kumar Adhikari (coordenator)
Luis Ever Young-S (collaborator)

INTRODUCTION:
At sufficiently low temperature and pressure the atoms become quantum particles and obey quantum statistics. These atoms could be bosons (H,⁴He,⁷Li etc) or fermions (³He,⁶Li etc). In the case of bosons, below a critical temperature one could have the formation of a new quantum state of matter called a Bose-Einstein condensate (BEC, predicted by Bose and Einstein), which exhibit many peculiar properties. The BEC is formed when a finite fraction of all the atoms fall into the lowest quantum orbital. The BEC exhibits superfluidity and is a fluid with no viscosity and when rotated it easily generates a lattice of vortices (first considered by Abrikosov). The properties of a weakly interacting dilute BEC can be described by a nonlinear Schrödinger equation written by Gross and Pitaevskii.

At low enough temperature (practically 0 K) all the fermions also fall into the lowest quantum orbitals obeying Pauli principle filling the quantum orbitals to a certain energy called Fermi energy. But such a system does not develop superfluidity unless there is an attractive atomic interaction. The superfluidity of a dilute gas of cold fermions in the presence of a weak atomic attraction was explained by Leggett (as suggested by Anderson) using the Bardeen-Cooper-Schrieffer (BCS) equation. (The BCS equation was used to explain superconductivity in case of charged fermionic electrons. Now it is realized that superconductivity and superfluidity are manifestations of the same fermionic phenomenon at low temperature. The manifestation is superfluidity for neutral atoms and superconductivity for charged particles.)

ACTUAL STATE OF AFFAIR:
As the superfluid phase of cold atoms are quantum objects and has large size of at least 10s of microns, we can observe and study many quantum processes in laboratory, which could otherwise be conceived in the context of atoms and fundamentamental particles in the imagination of theoreticians. Among these phenomena are quantum phase transition at 0 K without requiring heat, creation of coherent atom laser, generation of a vortex lattice, creation of a lattice of pure atoms to study solid state physics in a controlled fashion, etc. etc.

Such study is even more interesting in the case of fermions as our universe is constituted of fermions. Practically, all theories of the fermions from nuclear and hadronic physics to the study of neutron stars and black holes assume the limit of weak interactions. Now it is possible to reach the limit of strong interaction of cold superfluid fermions in laboratory using a Feshbach resonance. (Near a Feshbach resonance it is possible to easily increase the atomic interaction to a very large value and attain the limit of strongest interaction called unitarity.) This gives the opportunity test the applicability of existing theories in this limit.

MY CURRENT RESEARCH ACTIVITY
I presently study various properties of bosonic and fermionic superfluids, such as, superfluidity and other properties at unitarity, vortices and solitons in superfluids, Anderson localization of bosonic superfluids, Josephson oscillation and self trapping in superfluids, collapse in superfluids in the presence of attractive interaction, etc. etc.

1. Of special interest is the study of superfluidity in dipolar atoms with magnetic dipole moment interacting via angle-dependent anisotropic interaction. Because of this anisotropic interaction among dipolar atoms, the dipolar BEC has many peculiar properties. Below I describe two of my current activities.

(a) Solitons in dipolar BEC:
We are currently engaged in the study of soliton formation in BEC of dipolar atoms with large dipolar interaction. Normal solitons are formed for attractive atomic interaction. Because of peculiar properties of dipolar interaction strange things can happen. In the cigar-shaped elongated configuration the dipolar interaction leads to attraction, as many dipoles placed on a linear chain attract each other. Consequently, a cigar-shaped dipolar BEC could be attractive even for a finite repulsive atomic interaction. We have studied the dynamics of bright solitons formed in cigar-shaped dipolar BECs with repulsive atomic interactions. We also predicted vortex solitons in cigar-shaped dipolar BECs with repulsive atomic interactions and studied their collision dynamics. We find that the collision is elastic at large velocities of about 1 cm/s and two such solitons form a soliton molecule at low velocities.

Elastic collision of two bright and vortex solitons of dipolar BECs at high velocity of 1 cm/s

Molecule formation from two bright and vortex solitons of dipolar BECs placed side by side

(b) Anisotropic sound and shock waves in a dipolar BEC:
The interaction among the atoms in a BEC is essential for the propagation of sound (a noise or perturbation). The larger the interaction, the larger is the velocity of such propagation. However, the interaction in a dipolar BEC is direction dependent. As a consequence, sound and shock waves propagate in a dipolar condensate with different velocity in different directions. If we take the polarization of the dipoles along $z$ axis, the sound velocity is different along $x$ and $z$ directions. If a supersonic plane or bullet flies a shock wave with a Mach angle is generated. If in a uniform dipolar BEC a tiny object (laser) moves at supersonic speed a shock wave is generated. We studied the generation of this shock wave. If the tiny object moves with a fixed speed along $x$ or $z$ direction the shock waves are distinct in these case as can be seen in the following video. This theoretically studied effect might be expected in a dipolar BEC, but it is yet to be confirmed in experiment.