We present a lattice study of up to N = 20 unitary fermions confined to a harmonic trap. Our preliminary results show better than 1% agreement with high precision solutions to the many-body Schrodinger equation for up to N = 6. We are able to make predictions for larger N which were inaccessible by the Hamiltonian approach due to computational limitations. Harmonic traps are used experimentally to study cold atoms tuned to a Feshbach resonance. We show that they also provide certain benefits to numerical studies of many-body correlators on the lattice. In particular, we anticipate that the methods described here could be used for studying nuclear physics.We present a lattice study of up to N = 20 unitary fermions confined to a harmonic trap. Our preliminary results show better than 1% agreement with high precision solutions to the many-body Schrodinger equation for up to N = 6. We are able to make predictions for larger N which were inaccessible by the Hamiltonian approach due to computational limitations. Harmonic traps are used experimentally to study cold atoms tuned to a Feshbach resonance. We show that they also provide certain benefits to numerical studies of many-body correlators on the lattice. In particular, we anticipate that the methods described here could be used for studying nuclear physics.

Jun 16, 20230 citations

A new approach for studying large numbers of fermions in the unitary regime

Jong-Wan Lee, David B. Kaplan, Michael G. Endres +1 more

A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ0 = ≠/2. Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics. We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique. A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W. L.A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ0 = ≠/2. Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics. We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique. A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W. L.

Jun 16, 20230 citations

A new approach for studying large numbers of fermions in the unitary regime

Michael G. Endres, David B. Kaplan, Jong-Wan Lee +1 more

A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions.The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ 0 = π/2.Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics.We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique.A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W.L.A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions.The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ 0 = π/2.Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics.We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique.A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W.L.

arXiv:1011.3089International Symposium on Lattice Field Theory (LATTICE)Jun 6, 20111 citation

Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

Michael G. Endres, David B. Kaplan, Jong-Wan Lee +1 more

We present a lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions and apply it to a dilute gas of unitary fermions confined to a harmonic trap. In place of importance sampling, our approach makes use of high statistics, an improved action, and recently proposed statistical techniques. We show how improvement of the lattice action can remove discretization and finite volume errors systematically. For $N=3$ unitary fermions in a box, our errors in the energy scale as the inverse lattice volume, and we reproduce a previous high-precision benchmark calculation to within our $0.3%$ uncertainty; as additional benchmarks we reproduce precision calculations of $N=3,...,6$ unitary fermions in a harmonic trap to within our $\ensuremath{\sim}1%$ uncertainty. We then use this action to determine the ground-state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as ${64}^{3}\ifmmode\times\else\texttimes\fi{}72$. In contrast to variational calculations, we find evidence for persistent deviations from the thermodynamic limit for the range of $N$ considered.We present a lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions and apply it to a dilute gas of unitary fermions confined to a harmonic trap. In place of importance sampling, our approach makes use of high statistics, an improved action, and recently proposed statistical techniques. We show how improvement of the lattice action can remove discretization and finite volume errors systematically. For $N=3$ unitary fermions in a box, our errors in the energy scale as the inverse lattice volume, and we reproduce a previous high-precision benchmark calculation to within our $0.3%$ uncertainty; as additional benchmarks we reproduce precision calculations of $N=3,...,6$ unitary fermions in a harmonic trap to within our $\ensuremath{\sim}1%$ uncertainty. We then use this action to determine the ground-state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as ${64}^{3}\ifmmode\times\else\texttimes\fi{}72$. In contrast to variational calculations, we find evidence for persistent deviations from the thermodynamic limit for the range of $N$ considered.

arXiv:1106.5725Physical Review AOct 31, 201155 citations

Fermionization in one-dimensional cold atom systems

Jonathan Lindgren

Recent developments in experimental techniques have made it possible to use magnetic fields to tune interactions between trapped cold atoms with different spin components allowing for detailed experimental investigations of the properties of quantum mechanical few-body systems. In this thesis we investigate the properties of two-component cold atoms trapped in a harmonic oscillator potential with a zero range interaction of arbitrary strength between the different species. In the limit of infinite interaction the atoms will tend to avoid each other. This is reminiscent of the Pauli principle and we will address differences and similarities to a system of identical fermions. Exact diagonalization of the Hamiltonian in a harmonic oscillator basis is used to obtain the eigenvectors and eigenvalues of the system and we also employ numerical methods borrowed from nuclear physics to generate effective interactions using unitary transformations. This method proves to be very effective for improving the convergence and the computation time is significantly decreased even for very strongly interacting systems.Recent developments in experimental techniques have made it possible to use magnetic fields to tune interactions between trapped cold atoms with different spin components allowing for detailed experimental investigations of the properties of quantum mechanical few-body systems. In this thesis we investigate the properties of two-component cold atoms trapped in a harmonic oscillator potential with a zero range interaction of arbitrary strength between the different species. In the limit of infinite interaction the atoms will tend to avoid each other. This is reminiscent of the Pauli principle and we will address differences and similarities to a system of identical fermions. Exact diagonalization of the Hamiltonian in a harmonic oscillator basis is used to obtain the eigenvectors and eigenvalues of the system and we also employ numerical methods borrowed from nuclear physics to generate effective interactions using unitary transformations. This method proves to be very effective for improving the convergence and the computation time is significantly decreased even for very strongly interacting systems.

Jan 1, 20131 citation

Strongly Interacting Fermi Gases of Atoms Confined in a Harmonic Trap

Yeong E. Kim, Alexander L. Zubarev

Dynamics of strongly interacting Fermi gases, consisting of a 50-50 mixture of two different fermionic species, is investigated. For the equation of state we consider a Padé [2/2] approximations, which gives the weak-coupling perturbative formula (up to 4th order) in the low density regime, the unitary-limit Monte Carlo result in the high density regime, and reproduces the 4-fermion prediction for dimer-dimer scattering length in the BEC region. We use a time-dependent LDA to derive various properties of the Fermi gas under a harmonic confinement and compare them with the data of very recent experiments of 6Li atoms across a Feshbach resonance.Dynamics of strongly interacting Fermi gases, consisting of a 50-50 mixture of two different fermionic species, is investigated. For the equation of state we consider a Padé [2/2] approximations, which gives the weak-coupling perturbative formula (up to 4th order) in the low density regime, the unitary-limit Monte Carlo result in the high density regime, and reproduces the 4-fermion prediction for dimer-dimer scattering length in the BEC region. We use a time-dependent LDA to derive various properties of the Fermi gas under a harmonic confinement and compare them with the data of very recent experiments of 6Li atoms across a Feshbach resonance.

arXiv:cond-mat/0408283Aug 12, 20040 citations

N=3

unitary fermions in a box, our errors in the energy scale as the inverse lattice volume, and we reproduce a previous high-precision benchmark calculation to within our

0.3%

uncertainty; as additional benchmarks we reproduce precision calculations of

N=3,...,6

unitary fermions in a harmonic trap to within our $\ensuremath{\sim}1%$ uncertainty. We then use this action to determine the ground-state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as ${64}^{3}\ifmmode\times\else\texttimes\fi{}72$. In contrast to variational calculations, we find evidence for persistent deviations from the thermodynamic limit for the range of

N

considered.