| Collaborators |
My research in theoretical condensed matter physics falls in the area broadly
known as strongly correlated systems. The overarching goal is to understand
the wealth of phenomena exhibited by strongly interacting quantum matter.
A common thread in my research is the application and development of
quantum field theory approaches to these many body problems.
A brief outline of some of my research activities may be found below.
Ising Deconfinement Transition between Feshbach Resonant Superfluids
Phys. Rev. Lett. 106, 015303 (2011)
We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group (DMRG) and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary.
Collective Dynamics of Bose--Einstein Condensates in Optical Cavities
Phys. Rev. Lett. 105, 043001 (2010)
Recent experiments on Bose--Einstein condensates in optical
cavities have reported a quantum phase transition to a coherent state
of the matter-light system -- superradiance. The time dependent nature
of these experiments demands consideration of collective
dynamics. Here we establish a rich phase diagram, accessible by quench
experiments, with distinct regimes of dynamics separated by
non-equilibrium phase transitions. We include the key effects of
cavity leakage and the back-reaction of the cavity field on the
condensate. Proximity to some of these phase boundaries results in
critical slowing down of the decay of many-body oscillations. Notably,
this slow decay can be assisted by large cavity losses. Predictions
include the frequency of collective oscillations, a variety of
multi-phase co-existence regions, and persistent optomechanical
oscillations described by a damped driven pendulum. These findings
open new directions to study collective dynamics and non-equilibrium
phase transitions in matter-light systems.
Feshbach Resonance in Optical Lattices and the Quantum Ising Model
Phys. Rev. Lett. 103, 265302 (2009)
Motivated by experiments on heteronuclear Feshbach resonances
in Bose mixtures, we investigate s-wave pairing of two species of
bosons in an optical lattice. The zero temperature phase diagram
supports a rich array of superfluid and Mott phases and a network of
quantum critical points. This topology reveals an underlying structure
that is succinctly captured by a two-component Landau theory. Within
the second Mott lobe we establish a quantum phase transition described
by the paradigmatic longitudinal and transverse field Ising
model. This is confirmed by exact diagonalization of the 1D bosonic
Hamiltonian. We also find this transition in the homonuclear case.
Polaritons and Pairing Phenomena in Bose--Hubbard Mixtures
Phys. Rev. Lett. 102, 135301 (2009)
Motivated by recent experiments on cold atomic gases in ultra
high finesse optical cavities, we consider the problem of a two-band
Bose--Hubbard model coupled to quantum light. Photoexcitation promotes
carriers between the bands and we study the non-trivial interplay
between Mott insulating behavior and superfluidity. The model displays
a global U(1) X U(1) symmetry which supports the coexistence of Mott
insulating and superfluid phases, and yields a rich phase diagram with
multicritical points. This symmetry property is shared by several
other problems of current experimental interest, including
two-component Bose gases in optical lattices, and the bosonic BEC-BCS
crossover problem for atom-molecule mixtures induced by a Feshbach
resonance. We corroborate our findings by numerical simulations.
Magnetothermoelectric Response at a Superfluid--Mott
Phys. Rev. Lett. 98, 166801 (2007)
Since the discovery of high temperature
superconductivity, quantum phase transitions
between Mott insulators and superfluids/superconductors have been the focus
intense scrutiny. More recently, such transitions have been observed in
experiments on cold atomic gases. In collaboration with Prof. S. Sondhi and
Dr A. Green, we have examined the magnetothermoelectric response
insulator transitions in the ubiquitous Bose--Hubbard model. This work is motivated,
in part, by
Prof. P. Ong's
measurements in the cuprates. We use an approach based on
the quantum Boltzmann equation to investigate the response in the quantum critical regime.
Mott Insulators in Low Dimensions
Quite aside from their relevance to high temperature superconductivity,
Mott insulators are interesting because they lie outside the conventional
band theory of metals, insulators and semiconductors; according to band
theory Mott insulators ought to be metals.
These materials are rendered insulators by the Coulomb interaction between
electrons, and are a paradigmatic example of the impact of strong correlations. Quasi 1D Mott insulators, such as SrCuO2 and the Bechgaard salts,
are especially interesting because their collective excitations are quite
different from the electrons themselves. These novel "fractional''
excitations are termed spinons and holons and their existence has been
confirmed by neutron and x-ray scattering experiments. In collaboration with
Prof. F. Essler and A. Grage we have studied the magnetic correlations of 1D Mott insulators using field theory techniques.
Fractionalization from Frustration
An exciting feature of quantum many body systems is that the emergent
behaviour of the aggregate may be significantly richer than that of
its constituent particles. As in the 1D Mott insulator discussed
above, the collective many body excitations may have "fractional''
quantum numbers, which differ from those of the electron or
conventional spin waves. In collaboration with
Prof. A. Tsvelik,
we have investigated a family of spin ladder models where magnetic frustration
leads to fractionalization.
Phase Transitions and Disordered Systems
The modern theory of phase
transitions is highly developed, and an array of powerful theoretical tools
are commonly employed. New problems arise in systems with disorder,
such as those which exhibit the quantum Hall effect. A
significant component of my doctoral research was directed towards
the theory of second order phase transitions in low dimensional