In this thesis, I present the experimental realisation of the two-dimensional Hubbard model with ultracold fermionic Potassium-40 atoms in optical lattices. By tuning the dimensionality, kinetic and interaction in the optical lattices, we perform an analogue quantum simulation to explore the phase diagram of the Hubbard model. \n \nThe first key result is the experimental observation of particle-hole symmetry, namely a phase mapping between repulsive and attractive interactions. We compare a density-ordered, Mott-insulating phase with repulsive interaction to a spin-ordered, preformed pair phase and found excellent agreement with the theoretical prediction. The precise control and excellent detection capability of our quantum gas apparatus allow us to validate the particle-hole symmetry, and utilise it to explore quantum phases with a novel approach. \n \nNext, we investigate the spin-ordering on the repulsive side. By implementing a novel scheme based on coherent manipulation of spin correlations, we probe the anti-ferromagnetic ordering in the low-temperature phase diagram. The momentum-resolved spin correlations permit the reconstruction of spatial correlators without site-resolved imaging fidelity. \n \nFinally, we probe the attractive side of the phase diagram with a focus in pairing phenomenon, in which we draw a close analogy with BCS-BEC crossovers present in high-temperature superconducting cuprates and trapped ultracold Fermi gases. From the pair correlation function derived from thermodynamics observables, we observe the competition between the effective Pauli repulsion in fermionic systems and the on-site attraction we implemented.In this thesis, I present the experimental realisation of the two-dimensional Hubbard model with ultracold fermionic Potassium-40 atoms in optical lattices. By tuning the dimensionality, kinetic and interaction in the optical lattices, we perform an analogue quantum simulation to explore the phase diagram of the Hubbard model. \n \nThe first key result is the experimental observation of particle-hole symmetry, namely a phase mapping between repulsive and attractive interactions. We compare a density-ordered, Mott-insulating phase with repulsive interaction to a spin-ordered, preformed pair phase and found excellent agreement with the theoretical prediction. The precise control and excellent detection capability of our quantum gas apparatus allow us to validate the particle-hole symmetry, and utilise it to explore quantum phases with a novel approach. \n \nNext, we investigate the spin-ordering on the repulsive side. By implementing a novel scheme based on coherent manipulation of spin correlations, we probe the anti-ferromagnetic ordering in the low-temperature phase diagram. The momentum-resolved spin correlations permit the reconstruction of spatial correlators without site-resolved imaging fidelity. \n \nFinally, we probe the attractive side of the phase diagram with a focus in pairing phenomenon, in which we draw a close analogy with BCS-BEC crossovers present in high-temperature superconducting cuprates and trapped ultracold Fermi gases. From the pair correlation function derived from thermodynamics observables, we observe the competition between the effective Pauli repulsion in fermionic systems and the on-site attraction we implemented.

May 12, 20201 citation

Critical exponents for the sinh-cosh interaction model in the zero sector

Rudolf A. Römer, Bill Sutherland

In this paper, we continue our investigation of a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential s(s+1)/ ${\mathrm{sinh}}^{2}$ (r), while unlike particles interact with a pair potential -s(s+1)/ ${\mathrm{cosh}}^{2}$ (r). For an equal number of particles of the two components, the ground state for s>0 corresponds to an antiferromagnet/insulator. Excitations consist of a gapless pair-hole--pair continuum, a two-particle continuum with gap and excitons with gap. For -1s0, the system has two gapless excitations---a particle-hole continuum and a two-spin-wave continuum. Using finite-size scaling methods of conformal field theory, we calculate the asymptotic expressions and critical exponents for correlation functions of these gapless excitations at zero temperature. The conformal structure is closely related to the Hubbard model with repulsive on-site interaction.In this paper, we continue our investigation of a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential s(s+1)/${\mathrm{sinh}}^{2}$(r), while unlike particles interact with a pair potential -s(s+1)/${\mathrm{cosh}}^{2}$(r). For an equal number of particles of the two components, the ground state for s>0 corresponds to an antiferromagnet/insulator. Excitations consist of a gapless pair-hole--pair continuum, a two-particle continuum with gap and excitons with gap. For -1s0, the system has two gapless excitations---a particle-hole continuum and a two-spin-wave continuum. Using finite-size scaling methods of conformal field theory, we calculate the asymptotic expressions and critical exponents for correlation functions of these gapless excitations at zero temperature. The conformal structure is closely related to the Hubbard model with repulsive on-site interaction.

arXiv:cond-mat/9307021Physical review. B, Condensed matterMar 1, 19946 citations

Particle-hole interactions

Richard R. Chasman, John W. Durso

Nuclear Physics ADec 1, 19752 citations

Particle-hole entanglement of ultracold atoms in an optical lattice

H. T. Ng

We study the ground state of two-component bosonic atoms in a one-dimensional optical lattice. By applying an external field to the atoms at one end of the lattice, the atoms are transported and becomes localized at that site. The holes are then created in the remaining sites. The particle-hole superpositions are produced in this process. We investigate the entanglement entropy between the atoms in the two different parts of a lattice. A large degree of particle-hole entanglement is generated in the ground state. The particle-hole quantum correlations can be probed by the two-site parity correlation functions. The transport properties of the low-lying excited states are also discussed.We study the ground state of two-component bosonic atoms in a one-dimensional optical lattice. By applying an external field to the atoms at one end of the lattice, the atoms are transported and becomes localized at that site. The holes are then created in the remaining sites. The particle-hole superpositions are produced in this process. We investigate the entanglement entropy between the atoms in the two different parts of a lattice. A large degree of particle-hole entanglement is generated in the ground state. The particle-hole quantum correlations can be probed by the two-site parity correlation functions. The transport properties of the low-lying excited states are also discussed.

arXiv:1307.1541Physical Review AAug 28, 20130 citations

Two-particle correlation

A. K. Chaudhuri

Institute of Physics eBooksJan 1, 20140 citations

In this paper, we continue our investigation of a one-dimensional, two-component, quantum many-body system in which like particles interact with a pair potential s(s+1)/

{\mathrm{sinh}}^{2}

(r), while unlike particles interact with a pair potential -s(s+1)/

{\mathrm{cosh}}^{2}

(r). For an equal number of particles of the two components, the ground state for s>0 corresponds to an antiferromagnet/insulator. Excitations consist of a gapless pair-hole--pair continuum, a two-particle continuum with gap and excitons with gap. For -1s0, the system has two gapless excitations---a particle-hole continuum and a two-spin-wave continuum. Using finite-size scaling methods of conformal field theory, we calculate the asymptotic expressions and critical exponents for correlation functions of these gapless excitations at zero temperature. The conformal structure is closely related to the Hubbard model with repulsive on-site interaction.