Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1806.02948 · Physical Review A

Cooling fermions in an optical lattice by adiabatic demagnetization

Anthony E. Mirasola, Michael L. Wall, Kaden R. A. Hazzard

Published Sep 24, 2018• 3 citations
arXivHTMLPDF

Abstract

The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the N\'eel temperature. However, reaching this temperature in the laboratory has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the $\text{SU}(2)$ symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the $\text{SU}(2)$ symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low-temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low-temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard model.

DOI
10.1103/physreva.98.033607

Related papers

High-temperature properties of fermionic alkaline-earth-metal atoms in optical lattices

Kaden R. A. Hazzard, Victor Gurarie, Michael Hermele +1 more

We calculate experimentally relevant properties of trapped fermionic alkaline-earth-metal atoms in an optical lattice, modeled by the SU$(N)$ Hubbard model. We employ a high-temperature expansion that is accurate when the temperature is larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a noninteracting gas, as a function of initial gas temperature. Of particular experimental interest, we find that increasing $N$ for fixed particle numbers and initial temperatures gives substantially colder Mott insulators after the adiabatic ramping, up to more than a factor of 5 for relevant parameters. This cooling happens for all $N$, fixing the initial entropy, or for all $N\ensuremath{\lesssim}20$ (the exact value depends on dimensionality), at fixed, experimentally relevant initial temperatures.

arXiv:1011.0032•Physical Review A•Apr 26, 2012•51 citations

Adiabatic cooling of bosons in lattices to magnetically ordered quantum states

Johannes Schachenmayer, David Weld, Hirokazu Miyake +3 more

We suggest and analyze a scheme to adiabatically cool bosonic atoms to picokelvin temperatures which should allow the observation of magnetic ordering via superexchange in optical lattices. The starting point is a gapped phase called the spin Mott phase, where each site is occupied by one spin-up and one spin-down atom. An adiabatic ramp leads to an $xy$-ferromagnetic phase. We show that the combination of time-dependent density matrix renormalization group methods with quantum trajectories can be used to fully address possible experimental limitations due to decoherence, and demonstrate that the magnetic correlations are robust for experimentally realizable ramp speeds. Using a microscopic master equation treatment of light scattering in the many-particle system, we test the robustness of adiabatic state preparation against decoherence. Due to different ground-state symmetries, we also find a metastable state with $xy$-ferromagnetic order if the ramp crosses to regimes where the ground state is a $z$ ferromagnet. The bosonic spin Mott phase as the initial gapped state for adiabatic cooling has many features in common with a fermionic band insulator, but the use of bosons should enable experiments with substantially lower initial entropies.

arXiv:1503.07466•Physical Review A•Oct 14, 2015•27 citations

Quantum Adiabatic Doping with Incommensurate Optical Lattices

Jian Hui Lin, Jue Nan, Yuchen Luo +2 more

Quantum simulations of Fermi-Hubbard models have been attracting considerable effort in the optical lattice research, with the ultracold antiferromagnetic atomic phase reached at half filling in recent years. An unresolved issue is to dope the system while maintaining the low thermal entropy. Here we propose to achieve the low temperature phase of the doped Fermi-Hubbard model using incommensurate optical lattices through adiabatic quantum evolution. In this theoretical proposal, we find that one major problem about the adiabatic doping is atomic localization in the incommensurate lattice, potentially causing an exponential slowing down of the adiabatic procedure. We study both one- and two-dimensional incommensurate optical lattices, and find that the localization prevents efficient adiabatic doping in the strong lattice regime for both cases. With density matrix renormalization group calculation, we further show that the slowing down problem in one dimension can be circumvented by considering interaction induced many-body delocalization, which is experimentally feasible using Feshbach resonance techniques. This protocol is expected to be efficient as well in two dimensions where the localization phenomenon is less stable.

arXiv:1904.10553•Physical Review Letters•Dec 4, 2019•6 citations

Achieving the Néel state in an optical lattice

Arnaud Koetsier, R. A. Duine, Immanuel Bloch +1 more

We theoretically study the possibility of reaching the antiferromagnetic phase of the Hubbard model by starting from a normal gas of trapped fermionic atoms and adiabatically ramping up an optical lattice. Requirements on the initial temperature and the number of atoms are determined for a three-dimensional square lattice by evaluating the N\'eel state entropy, taking into account fluctuations around the mean-field solution. We find that these fluctuations place important limitations on adiabatically reaching the N\'eel state.

arXiv:0711.3425•Physical Review A•Feb 25, 2008•45 citations

Sudden and Slow Quenches into the Antiferromagnetic Phase of Ultracold Fermions

Monika Ojekhile, Robert Höppner, Henning Moritz +1 more

Abstract We propose a method to reach the antiferromagnetic state of two-dimensional Fermi gases trapped in optical lattices: Independent subsystems are prepared in suitable initial states and then connected by a sudden or slow quench of the tunneling between the subsystems. Examples of suitable low-entropy subsystems are double wells or plaquettes, which can be experimentally realised in Mott insulating shells using optical super-lattices. We estimate the effective temperature T* of the system after the quench by calculating the distribution of excitations created using the spin wave approximation in a Heisenberg model. We investigate the effect of an initial staggered magnetic field and find that for an optimal polarisation of the initial state the effective temperature can be significantly reduced from T*≈1.7 T c at zero polarisation to T*<0.65T c, where T c is the crossover temperature to the antiferromagnetic state. The temperature can be further reduced using a finite quench time. We also show that T* decreases logarithmically with the linear size of the subsystem.

arXiv:1308.5680•Zeitschrift für Naturforschung A•Nov 2, 2016•1 citation

Quantum phases in Fermi Hubbard systems with tunable frustration

Xu, Muqing

Analog quantum simulation provides a unique toolkit to investigate quantum many-body problems of whose solutions may be incredibly challenging. In particular, using ultracold fermionic atoms in optical lattices it realizes the Fermi Hubbard model, which is a fundamental model in condensed matter physics exhibiting properties relevant to many intriguing strongly-correlated systems. However, most quantum simulators of the Hubbard model have so far restricted to the square geometries. In addition, access to low temperatures where the exotic quantum phases are predicted to develop has still remained elusive. In this thesis, we engineer a novel optical lattice with dynamically tunable geometries and significantly reduced technical noises. We extend for the first time the study of quantum magnetism into the exotic phases in a Fermi Hubbard system with tunable geometric frustration. As we continuously tune our system from a square to a triangular lattice geometry, we observe a transition from a Néel antiferromagnet to a 120-degree spin spiral state. We then study, again for the first time, how doping affects a frustrated quantum magnet. To our surprise, we found an emergent ferromagnetic state with strong particle doping, which is absent on the hole-doped side and is in stark contrast with the particle-hole symmetric doping dependence in a square lattice. To shed light on the role of itinerant dopants in the emergence of these new magnetic properties, we furthermore leverage the unique single-particle resolution capabilities of our platform to probe higher-order density and spin correlations. These measurements hint at a new type of magnetism induced by kinetic frustration, which manifests as local antiferromagnetic correlations around hole dopants and and ferromagnetic correlations around particle dopants. Unlike magnetism induced by exchange or superexchange interactions, the energy associated with this mechanism is the kinetic energy, closely related to the famous rigorous results by Nagaoka. Furthermore, the dynamical tunability of the lattice allows adibatic engineering of quantum states in optical lattices. We discuss the preliminery efforts to prepare strongly-correlated states with significantly reduced temperatures, which may pave the way towards low temperature states in the Hubbard model.

•Jan 1, 2024•0 citations
The Fermi-Hubbard model describes ultracold fermions in an optical lattice and exhibits antiferromagnetic long-ranged order below the N'eel temperature. However, reaching this temperature in the laboratory has remained an elusive goal. In other atomic systems, such as trapped ions, low temperatures have been successfully obtained by adiabatic demagnetization, in which a strong effective magnetic field is applied to a spin-polarized system and the magnetic field is adiabatically reduced to zero. Unfortunately, applying this approach to the Fermi-Hubbard model encounters a fundamental obstacle: the SU(2)\text{SU}(2)SU(2) symmetry introduces many level crossings that prevent the system from reaching the ground state, even in principle. However, by breaking the SU(2)\text{SU}(2)SU(2) symmetry with a spin-dependent tunneling, we show that adiabatic demagnetization can achieve low-temperature states. Using density matrix renormalization group (DMRG) calculations in one dimension, we numerically find that demagnetization protocols successfully reach low-temperature states of a spin-anisotropic Hubbard model, and we discuss how to optimize this protocol for experimental viability. By subsequently ramping spin-dependent tunnelings to spin-independent tunnelings, we expect that our protocol can be employed to produce low-temperature states of the Fermi-Hubbard model.
We calculate experimentally relevant properties of trapped fermionic alkaline-earth-metal atoms in an optical lattice, modeled by the SU(N)(N)(N) Hubbard model. We employ a high-temperature expansion that is accurate when the temperature is larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a noninteracting gas, as a function of initial gas temperature. Of particular experimental interest, we find that increasing NNN for fixed particle numbers and initial temperatures gives substantially colder Mott insulators after the adiabatic ramping, up to more than a factor of 5 for relevant parameters. This cooling happens for all NNN, fixing the initial entropy, or for all $N\ensuremath{\lesssim}20$ (the exact value depends on dimensionality), at fixed, experimentally relevant initial temperatures.
We suggest and analyze a scheme to adiabatically cool bosonic atoms to picokelvin temperatures which should allow the observation of magnetic ordering via superexchange in optical lattices. The starting point is a gapped phase called the spin Mott phase, where each site is occupied by one spin-up and one spin-down atom. An adiabatic ramp leads to an xyxyxy-ferromagnetic phase. We show that the combination of time-dependent density matrix renormalization group methods with quantum trajectories can be used to fully address possible experimental limitations due to decoherence, and demonstrate that the magnetic correlations are robust for experimentally realizable ramp speeds. Using a microscopic master equation treatment of light scattering in the many-particle system, we test the robustness of adiabatic state preparation against decoherence. Due to different ground-state symmetries, we also find a metastable state with xyxyxy-ferromagnetic order if the ramp crosses to regimes where the ground state is a zzz ferromagnet. The bosonic spin Mott phase as the initial gapped state for adiabatic cooling has many features in common with a fermionic band insulator, but the use of bosons should enable experiments with substantially lower initial entropies.
Quantum simulations of Fermi-Hubbard models have been attracting considerable effort in the optical lattice research, with the ultracold antiferromagnetic atomic phase reached at half filling in recent years. An unresolved issue is to dope the system while maintaining the low thermal entropy. Here we propose to achieve the low temperature phase of the doped Fermi-Hubbard model using incommensurate optical lattices through adiabatic quantum evolution. In this theoretical proposal, we find that one major problem about the adiabatic doping is atomic localization in the incommensurate lattice, potentially causing an exponential slowing down of the adiabatic procedure. We study both one- and two-dimensional incommensurate optical lattices, and find that the localization prevents efficient adiabatic doping in the strong lattice regime for both cases. With density matrix renormalization group calculation, we further show that the slowing down problem in one dimension can be circumvented by considering interaction induced many-body delocalization, which is experimentally feasible using Feshbach resonance techniques. This protocol is expected to be efficient as well in two dimensions where the localization phenomenon is less stable.
We theoretically study the possibility of reaching the antiferromagnetic phase of the Hubbard model by starting from a normal gas of trapped fermionic atoms and adiabatically ramping up an optical lattice. Requirements on the initial temperature and the number of atoms are determined for a three-dimensional square lattice by evaluating the N\'eel state entropy, taking into account fluctuations around the mean-field solution. We find that these fluctuations place important limitations on adiabatically reaching the N\'eel state.
Abstract We propose a method to reach the antiferromagnetic state of two-dimensional Fermi gases trapped in optical lattices: Independent subsystems are prepared in suitable initial states and then connected by a sudden or slow quench of the tunneling between the subsystems. Examples of suitable low-entropy subsystems are double wells or plaquettes, which can be experimentally realised in Mott insulating shells using optical super-lattices. We estimate the effective temperature T* of the system after the quench by calculating the distribution of excitations created using the spin wave approximation in a Heisenberg model. We investigate the effect of an initial staggered magnetic field and find that for an optimal polarisation of the initial state the effective temperature can be significantly reduced from T*≈1.7 T c at zero polarisation to T*<0.65T c, where T c is the crossover temperature to the antiferromagnetic state. The temperature can be further reduced using a finite quench time. We also show that T* decreases logarithmically with the linear size of the subsystem.
Analog quantum simulation provides a unique toolkit to investigate quantum many-body problems of whose solutions may be incredibly challenging. In particular, using ultracold fermionic atoms in optical lattices it realizes the Fermi Hubbard model, which is a fundamental model in condensed matter physics exhibiting properties relevant to many intriguing strongly-correlated systems. However, most quantum simulators of the Hubbard model have so far restricted to the square geometries. In addition, access to low temperatures where the exotic quantum phases are predicted to develop has still remained elusive. In this thesis, we engineer a novel optical lattice with dynamically tunable geometries and significantly reduced technical noises. We extend for the first time the study of quantum magnetism into the exotic phases in a Fermi Hubbard system with tunable geometric frustration. As we continuously tune our system from a square to a triangular lattice geometry, we observe a transition from a Néel antiferromagnet to a 120-degree spin spiral state. We then study, again for the first time, how doping affects a frustrated quantum magnet. To our surprise, we found an emergent ferromagnetic state with strong particle doping, which is absent on the hole-doped side and is in stark contrast with the particle-hole symmetric doping dependence in a square lattice. To shed light on the role of itinerant dopants in the emergence of these new magnetic properties, we furthermore leverage the unique single-particle resolution capabilities of our platform to probe higher-order density and spin correlations. These measurements hint at a new type of magnetism induced by kinetic frustration, which manifests as local antiferromagnetic correlations around hole dopants and and ferromagnetic correlations around particle dopants. Unlike magnetism induced by exchange or superexchange interactions, the energy associated with this mechanism is the kinetic energy, closely related to the famous rigorous results by Nagaoka. Furthermore, the dynamical tunability of the lattice allows adibatic engineering of quantum states in optical lattices. We discuss the preliminery efforts to prepare strongly-correlated states with significantly reduced temperatures, which may pave the way towards low temperature states in the Hubbard model.