Ultracold atomic physics
Ultra-cold atomic physics is a recent field, having only emerged in the past decade at the intersection of atomic/molecular physics and condensed matter physics. Some of the big questions we ask are related to the new kinds of ways in which atoms get organized at low temperatures. Specifically, we work to understand quantum phase transitions between two fundamentally different ground states at zero temperature. Some of the problems that we are studying are: (1) In the continuum, we are examining the transition from a gas of bosons and fermions (BEC + atomic Fermi surface) to composite fermions (molecular Fermi surface, no condensate) as the interaction between the two species increases. (2) With an optical lattice, we study a quantum phase transition between superfluid and Mott insulator states driven by increasing the repulsive interactions between bosons. (3) In fermionic systems with repulsive interactions, it is possible to see the emergence of a Mott insulator with a gap to charge excitations and antiferromagnetic order. (4) Fermions with intermediate to strong attractive interactions have a clear separation between the temperature at which pairing between fermions sets in and the temperature where pairs develop long range phase coherence. If the number of up and down pairs are unequal, there is the possibility of FFLO states in which the pairing amplitude is modulated spatially. These are discussed in more detail below.
Bose Fermi Mixtures
Mixtures of particles with different statistics sounds novel in condensed matter physics, but actually occurs in many systems where fermionic electrons or quasiparticles interact with bosonic collective excitations like phonons and magnons. We specifically consider this problem in the cold-atom context, where Feshbach resonances enable the boson-fermion interaction to be tuned from extremely small to extremely strong. The limiting cases are easily identified as a weakly depleted Bose-Einstein condensate (BEC) of bosons and an essentially perfect Fermi sea, and a gas of composite fermionic molecules that form a Fermi sea with no BEC for strong interactions. Using variational and diffusion quantum Monte Carlo technique, we are currently mapping the phases and quantum phase transitions at intermediate couplings. There are strong hints of an intermediate fermion superfluid with p-wave pairing coexisting with a BEC.
Publications: Paper in preparation.
Bose Hubbard Models with Synthetic Spin-Orbit Coupling: Mott Insulators, Spin Textures and Superfluidity
Artificial gauge fields in cold atom systems can give rise to exotic states of matter, and open the exciting realm of topological insulators and superfluids to highly controlled experiments. In this work we investigated the magnetic correlations in the Mott-insulating and superfluid phases of two-component bosons with spin-orbit coupling in an optical lattice, and we uncovered a variety of exotic states. We further found that the separation of spin and charge order can be understood by introducing a slave-boson theory, inspired by similar physics in strongly correlated electron systems.
- William S. Cole, Shizhong Zhang, Arun Paramekanti, Nandini Trivedi, Phys. Rev. Lett. 109, 085302 (2012)
Interferometric detection of modulated superfluidity
A system with unequal populations of up and down fermions may exhibit a Larkin-Ovchinnikov (LO) phase characterized by periodic domain walls across which the order parameter changes sign and the excess polarization is localized. This fascinating example of self-organized quantum matter has long been sought after in exotic superconductors and in ultracold atomic gases, and it may even occur in neutron stars. But despite fifty years of theoretical and experimental work, there has so far been no unambiguous observation of an LO phase. We have analyzed the consequences of an experiment in which two fermion clouds, prepared with unequal populations, are allowed to expand and interfere. We show that a pattern of staggered fringes in the interference is unequivocal evidence of LO physics.
- Mason Swanson, Yen Lee Loh, and Nandini Trivedi, New J. Phys. 14 033036 (2012)
Bose Hubbard Model on optical lattices
Ultra-cold atom systems are a remarkable opportunity to study crystals with effectively perfect ordering or with user-controlled disorder on a microscopic scale. Ultimately the goal is to emulate real materials with experimental systems and discern the phases of matter within them but first these systems must be fully understood and characterized. The Bose-Hubbard model (BHM) that describes bosons moving through a lattice with on-site repulsion is the simplest strongly interacting test case. Our group has extensively studied the phases of and the low-lying excitations in the BHM and sharpened the connection between experimental observables and the underlying quantum phase.
One of the key insights to emerge from this work is that the presence of the overall harmonic trapping potential can be exploited to more efficiently map the finite-temperature phase diagram.
- Yasuyuki Kato, Qi Zhou, Naoki Kawashima and Nandini Trivedi, Nature Physics 4, 617-621 (2008).
- Qi Zhou, Yasuyuki Kato, Naoki Kawashima and Nandini Trivedi. Phys. Rev. Lett. 103 085701 (2009).
- Mahmud Khan, Eric Duchon, Yasuyuki Kato, Naoki Kawashima, Nandini Trivedi, Richard Scalettar, Phys. Rev. B 84, 054302 (2011).
- Eric Duchon, Yasuyuki Kato, Nandini Trivedi, Phys. Rev. A 86, 063608 (2012).