Quantum Magnetism with Mesoscopic Bose-Einstein Condensates

Abstract

Lattice gases in the strongly correlated regime have been proven to simulate quantum magnetic models under certain conditions: the mapping of the double-well system onto the Lipkin-Meshkov-Glick spin model is a paradigmatic case. A suitable definition of the length in the Hilbert space of the system leads to the concept of a correlation length, whose divergence is a characteristic property of continuous quantum phase transitions. We calculate the finite-size scaling of some observables like e.g. the magnetization or the population imbalance, as well as of the Schmidt gap, obtaining in this way the critical exponents associated to such transitions. The systematic definition of the Schmidt gap in extended Hamiltonians provides a good tool to analyze the set of critical exponents associated to transitions in systems formed by a larger number of traps. This demonstrates, thus, the potential use of mesoscopic Bose-Einstein condensates as quantum simulators of condensed matter systems.

6 pages. 4 figures. arXiv admin note: text overlap with arXiv:1411.6004

References in corpus (23)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Cold bosonic atoms in optical lattices
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1-D optical lattices
• Short-range quantum magnetism of ultracold fermions in an optical lattice
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains
• Phase diagram of the three-dimensional Hubbard model at half filling
• Scaling of the entanglement spectrum near quantum phase transitions
• Mesoscopic ensembles of polar bosons in triple-well potentials
• Macroscopic self trapping in BECs: analysis of a dynamical quantum phase transition
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• A dipolar self-induced bosonic Josephson junction
• Quantum Criticality in a Bosonic Josephson Junction
• Fragmented condensation in Bose-Hubbard trimers with tunable tunnelling
• Entanglement entropy and macroscopic quantum states with dipolar bosons in a triple-well potential
• Quantum phase transition and critical fluctuations of an attractive Bose gas in a double well potential
• The role of anisotropy in dipolar bosons in triple-well potentials
• Macroscopic superposition states of ultracold bosons in a double-well potential

Cited by in corpus (11)

• Order parameter and detection for crystallized dipolar bosons in lattices
• Correlations of strongly interacting ultracold dipolar bosons in optical lattices
• Extended Bose-Hubbard Model with dipolar and contact interactions
• Detecting One-Dimensional Dipolar Bosonic Crystal Orders via Full Distribution Functions
• Euler top with a rotor: classical analogies of spin squeezing and quantum phase transitions in a generalized Lipkin-Meshkov-Glick model
• Ensemble inequivalence in long-range quantum systems
• Symmetries and boundary conditions with a twist
• Schmidt gap in random spin chains
• Correlation dynamics of dipolar bosons in 1D triple well optical lattice
• Ensemble Inequivalence in Long-Range Quantum Spin Systems
• Certification of spin-based quantum simulators