Optically trapped atoms have opened up an entirely new vista for studying phase transitions in quantum systems with an unprecedented control of parameters like the particle density, interaction strength, etc. At the same time, new issues such as the effects of the confining potential on the critical behavior need to be addressed. We are studying the details of the Mott and superfluid phases in trapped atom systems (bosons in a confining potential).

Projects include many fascinating features of these systems including the unusual behavior of `visibility' as one increases the interaction strength, soliton formation, and the possibility of novel `FFLO' superconducting phases when the numbers of spin up and spin down fermionic atoms are different.

Relevant Publications:

[105.] F. Hebert, G.G. Batrouni R.T. Scalettar G. Schmid, M. Troyer and A. Dorneich, ``Quantum phase transitions in the two-dimensional hardcore boson model,'' Phys. Rev. B65, 014513 (2002)
[115.] G.G. Batrouni, V. Rousseau, R.T. Scalettar, M. Rigol, A. Muramatsu, and P.J.H. Denteneer, ``Mott Domains of Bosons Confined on Optical Lattices,'' Phys. Rev. Lett. 89, 117203 (2002).
[123.] M. Rigol, A. Muramatsu, G.G. Batrouni, V. Rousseau, R.T. Scalettar, P.J.H. Denteneer, and M. Troyer, "Mott Domains of bosons and fermions confined in optical lattices,'' Course in the Physics of Correlated Electron Systems and High-Tc Superconductors, Vietri sul Mare (Salerno), Italy, 14 - 25 October 2002.
[127.] M. Rigol, A. Muramatsu, G.G. Batrouni, and R.T. Scalettar, "Local quantum criticality in confined fermions on optical lattices,'' Phys. Rev. Lett. 91, 130403 (2003).
[132.] V. Rousseau, G. G. Batrouni, and R.T. Scalettar, "Phase separation in the bosonic Hubbard model with ring exchange," Phys. Rev. Lett. 93, 110404 (2004).
[137.] M. Rigol, A. Muramatsu, G.G. Batrouni, and R.T. Scalettar, "Local Mott metal-insulator transition in confined fermions on optical lattices," AIP Conf. Proc. 715, 225-234 (2004).
[139.] F. Hebert, G.G. Batrouni, and R. T. Scalettar, "Solitons in Trapped Bose-Einstein condensates in one-dimensional optical lattices," Phys. Rev. A71, 063609 (2005).
[140.] R. T. Scalettar, G. Batrouni, P. Denteneer, F. H\'ebert, A. Muramatsu, M. Rigol, V. Rousseau, and M. Troyer, "Equilibrium and Dynamical Properties of the Boson Hubbard Model in One Dimension," J. Low Temp. Phys. 140, 315 (2005).
[141.] M. Rigol, S. R. Manmana, A. Muramatsu, R. T. Scalettar, R. R. P. Singh, and S. Wessel, "Comment on `Novel Superfluidity in a Trapped Gas of Fermi Atoms with Repulsive Interaction Loaded on an Optical Lattice'", Phys. Rev. Lett. 95, 218901 (2005).
[143.] G.G. Batrouni, F.F. Assaad, R.T. Scalettar, P.J.H. Denteneer, "Dynamic response of trapped ultracold bosons on optical lattices," Phys. Rev. A72, R031601 (2005).
[144.] M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective Oscillations of Strongly Correlated 1D Bosons on a Lattice," Phys. Rev. Lett. 95, 110402 (2005).
[150.] M. Rigol, V. Rousseau, R.T. Scalettar, and R.R.P. Singh, "Dipolar Oscillations of Strongly Correlated Bosons on a One-Dimensional Lattice," Proceedings of the 24th International Conference on Low Temperature Physics, Orlando, Florida, USA, August, 2005.
[152.] P. Sengupta, M. Rigol, G. G. Batrouni, P. J. H. Denteneer, and R. T. Scalettar, "Phase coherence, visibility, and the superfluid--Mott-insulator transition on one-dimensional optical lattices," Phys. Rev. Lett. 95, 220402 (2005).
[154.] M. Rigol, R. T. Scalettar, G. G. Batrouni, and P. Sengupta, "Time of flight experiments and the formation of Mott domains of fermions and bosons on optical lattices," Phys. Rev. B73, 121103(R) (2006).
[155.] M. Rigol, A. Muramatsu, G. G. Batrouni, V. Rousseau, R. T. Scalettar, P. J. H. Denteneer, and M. Troyer, "Mott domains of bosons and fermions confined in optical lattices," AIP Conf. Proc. 678, 283 (2003).
[159.] V.G. Rousseau, M. Rigol, F. Hebert, D.P. Arovas, G.G. Batrouni, and R.T. Scalettar, "Exact Study of the 1D Boson Hubbard Model with a Superlattice Potential," Phys. Rev. B73, 174516 (2006).
[165.] R.T. Scalettar, M. Rigol, V.G. Rousseau, P. Sengupta, G.G. Batrouni, F. Hebert, P.J.H. Denteneer, A. Muramatsu, and M. Troyer, "Phase Diagram and Visibility of Optically Trapped Bosons," AIP Conf. Proc. 816, 232 (2006).
[174.] G.G. Batrouni, M.H. Huntley, V.G. Rousseau and R.T. Scalettar, "Exact Numerical Study of Pair Formation with Imbalanced Fermion Populations," Phys. Rev. Lett. 100, 116405 (2008).
[176.] V.G. Rousseau, A. Baldwin, A. Zujev, P.J.H. Denteneer, M. Rigol, and R.T. Scalettar, Superfluid and Mott Insulator Phases of one dimensional Bose-Fermi Mixtures, Phys. Rev. A78, 033619 (2008).
[177.] C.N. Varney, V. Rousseau, and R.T. Scalettar, "Quantum Monte Carlo study of the visibility of one-dimensional Bose-Fermi mixtures," Phys. Rev. A77, 041608 (2008).
[179.] G.G. Batrouni, H.R. Krishnamurthy, K.W. Mahmud, V.G. Rousseau, and R.T. Scalettar, "Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap," Phys. Rev. A78 023627 (2008).
[184.] G.G. Batrouni, V.G. Rousseau, and R.T. Scalettar, "Magnetic and Superfluid Transitions in the d=1 Spin-1 Boson Hubbard Model," Phys. Rev. Lett. 102, 140402 (2009).
[185.] Marcos Rigol, George G. Batrouni, Valery G.~Rousseau, and Richard T. Scalettar, "Universal state diagrams for harmonically trapped bosons in optical lattices," Phys. Rev. A79, 053605 (2009).
[189.] T. Paiva, R.T. Scalettar, M. Randeria, and N. Trivedi, "Fermions in 2D Optical Lattices: Constraints on entropy for observing antiferromagnetism and superfluidity," submitted to Phys. Rev. Lett.
[187.] C.N. Varney, C.R.~Lee, Z.J. Bai, S. Chiesa, M. Jarrell, and R. T. Scalettar, "High Precision Quantum Monte Carlo Study of the 2D Fermion Hubbard Model at Half-Filling", Phys. Rev. B80, 075116 (2009).