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

Expansion dynamics in fermionic quantum gases

J. Kajala

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In this work we study dynamics of fermionic quantum gases. Radio frequency spectroscopy, Josephson oscillations, and time-of-flight dynamics are studied theoretically, and with the help of numerical simulations using the time-evolving block decimation algorithm. \n The simulations of radio frequency spectroscopy shed light on the nature of excitations in a fermionic superfluid confined in a lattice. The Josephson oscillations in the presence of different potentials for up and down spins show that the asymmetric Josephson effect cannot be described by the traditionally established view of coherent tunnelling of Cooper pairs. The expansion dynamics of a band-insulating state reveals that we can explain the time development of two-component systems in a lattice using a simple two-site model. Finally, the time-of-flight expansion of an imbalanced superfluid restricted to move in one dimension provides a remarkably simple way for detecting the long-sought-for Fulde-Ferrell-Larkin-Ovchinnikov superfluid state.

Related papers

Expansion of 1D Polarized Superfluids: The Fulde-Ferrell-Larkin-Ovchinnikov State Reveals Itself

Hong Bing Lu, Leslie O. Baksmaty, C. J. Bolech +1 more

We study the expansion dynamics of a one-dimensional polarized Fermi gas after its sudden release from confinement using both the mean-field Bogoliubov-de Gennes and the numerically unbiased time-evolving block decimation methods. Our results show that experimentally observable spin density modulations, directly related to the presence of a Fulde-Ferrell-Larkin-Ovchinnikov state, develop during the expansion of the cloud. Our work therefore provides a robust theoretical proposal for the detection of this long-sought state.

arXiv:1202.3935•Physical Review Letters•May 29, 2012•36 citations

Making a spin-difference in quantum gases

Miikka O. J. Heikkinen

This thesis studies the theory of quantum gases. We focus on fermionic superfluidity in systems in which the control over the spin degree of freedom has a central role. \nWe explain the microscopic origin of the spin-asymmetric Josephon effect, and propose methods for realizing this effect experimentally in quantum gases. \nWe investigate the phenomenon of fermionic superfluidity in the presence of spin-polarization, with our main focus on the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase. We show that the FFLO pairing mechanism leads to an anisotropic speed of sound which can be used to identify the state in experiments. Using real-space dynamical mean field theory (DMFT), we compute the phase diagram of a trapped, spin-polarized Fermi gas in a dimensional crossover from a 1D to a 3D optical lattice. We find that the FFLO state is realized in a broad region of parameters throughout the crossover while the shell structure of the Fermi gas preceding the transition to the full FFLO state shows a strong dependence on the dimensionality. Finally, we utilize the cluster DMFT method to show that the FFLO state is stable against non-local quantum fluctuations even though these fluctuations do affect the critical temperature of the state.

•Jan 1, 2014•1 citation

Searching For FFLO States in Ultracold Polarized Fermi Gases: A Numerical Approach

Lu, Hong

Ultracold atomic gases have emerged as an ideal laboratory system to emulate many-body physics in an unprecedentedly controllable manner. Numerous many-body quantum states and phases have been experimentally explored and characterized using the ultracold atomic gases, offering new insights into many exciting physics ranging from condensed matters to cosmology. In this thesis, we will present a systematic numerical study of a novel experimental system, population imbalanced two-component ultracold Fermi gases. We explore the phase diagram of this system in both 3D and 1D especially focusing on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by a spatially oscillating order parameter. In 3D, we solve for the stationary states of trapped imbalanced Fermi gases in a wide range of parameter space with a home-made parallel eigen-solver for Bogoliubov-de Gennes (BdG) equations. Our results show that there exists a metastable state with a FFLO type oscillating order parameter. In 1D, we simulate the dynamical expansion of the population imbalanced Fermi gases from the trap. A numerically quasi-exact scheme, time-evolving block decimation (TEBD), is introduced for the comparative studies with the solution of the time-dependent BdG equation. Our results predict that the existence of FFLO states will leave conspicuous signatures in the density profiles during the expansion. For further understanding of the interplay between the population imbalance and two-body pairing interaction between two spin components, we also study the spin transport properties through trapped ultracold Fermi gases. The preliminary results will be discussed.

•Dec 1, 2012•0 citations

Spin-asymmetrinen Josephsonin ilmiö optisissa superhiloissa

Kreula, Juha

This work considers the theory of ultracold Fermi gases. We study the spin-asymmetric Josephson effect where the spin components of a Cooper pair feel spin-dependent potentials during the tunneling process and as a result oscillate at the same Josephson frequency but with different amplitudes. This contrasts the conventional interpretation of the Josephson effect in which the Cooper-paired spins 'tunnel together'. Here, we propose a new experimental arrangement to detect the yet-unobserved spin-asymmetric Josephson effect. We investigate two-component fermions in a one-dimensional spin-dependent optical superlattice described by a Fermi-Hubbard Hamiltonian and simulate the dynamics of the set-up with the essentially exact time-evolving block decimation (TEBD) numerical method. We demonstrate that the characteristics of the spin-asymmetric Josephson effect, frequency-synchronized particle number oscillations with spin-asymmetric critical currents, are present in the system. We show that the Josephson frequency depends only on the sum of the spin-dependent potential offsets between two adjacent sites in the super-lattice. We further exhibit that significant asymmetries of over 10% in the critical currents of the spin components are feasible. We also evince that the properties of the particle currents in the super-lattice system agree with the analytical results given by a Hubbard dimer model consisting of only one unit cell of the super-lattice in the strongly interacting limit.

•Jan 1, 2013•0 citations

Collective excitations in ultracold Fermi gases

Anna Korolyuk

Ultracold gases are of great interest in modern physics. The main reason is that in the systems of ultracold gases the parameters can be easily tuned, thus they can be used as a testing ground for various quantum many-body theories. Interesting macroscopic quantum effects have been observed in the ultracold gas systems, for instance Bose-Einstein condensation. In this thesis, theoretical knowledge of ultracold gases is extended. A summary of the methods used in this thesis is given, including a detailed description of the density response theory and the time-evolving block decimation (TEBD) algorithm. Collective excitations of an ultracold gas in a three-dimensional (3D) spherically symmetric trap are studied in detail in publications II and III. As a result, several collective modes are discovered such as a low energy Higgs-type mode, a second sound-like mode, and a strong mode resembling the Leggett mode. Using the TEBD algorithm, physics of a polaron in a one-dimensional (1D) lattice, and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in 1D are studied in publications IV and I, respectively. In publication I a method to detect the FFLO phase is suggested, namely by the observation of the change in the double occupancy after a lattice depth modulation. Publication IV compares a variational ansatz and the TEBD simulations and finds an excellent agreement, indicating that the variational ansatz can be used to describe the system for a certain range of interactions.

•Jan 1, 2014•0 citations

Expansion Dynamics in the One-Dimensional Fermi-Hubbard Model

J. Kajala, Francesco Massel, Päivi Törmä

Expansion dynamics of interacting fermions in a lattice is simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and nonpaired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.

arXiv:1101.6025•Physical Review Letters•May 16, 2011•51 citations
In this work we study dynamics of fermionic quantum gases. Radio frequency spectroscopy, Josephson oscillations, and time-of-flight dynamics are studied theoretically, and with the help of numerical simulations using the time-evolving block decimation algorithm. \n The simulations of radio frequency spectroscopy shed light on the nature of excitations in a fermionic superfluid confined in a lattice. The Josephson oscillations in the presence of different potentials for up and down spins show that the asymmetric Josephson effect cannot be described by the traditionally established view of coherent tunnelling of Cooper pairs. The expansion dynamics of a band-insulating state reveals that we can explain the time development of two-component systems in a lattice using a simple two-site model. Finally, the time-of-flight expansion of an imbalanced superfluid restricted to move in one dimension provides a remarkably simple way for detecting the long-sought-for Fulde-Ferrell-Larkin-Ovchinnikov superfluid state.
We study the expansion dynamics of a one-dimensional polarized Fermi gas after its sudden release from confinement using both the mean-field Bogoliubov-de Gennes and the numerically unbiased time-evolving block decimation methods. Our results show that experimentally observable spin density modulations, directly related to the presence of a Fulde-Ferrell-Larkin-Ovchinnikov state, develop during the expansion of the cloud. Our work therefore provides a robust theoretical proposal for the detection of this long-sought state.
This thesis studies the theory of quantum gases. We focus on fermionic superfluidity in systems in which the control over the spin degree of freedom has a central role. \nWe explain the microscopic origin of the spin-asymmetric Josephon effect, and propose methods for realizing this effect experimentally in quantum gases. \nWe investigate the phenomenon of fermionic superfluidity in the presence of spin-polarization, with our main focus on the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase. We show that the FFLO pairing mechanism leads to an anisotropic speed of sound which can be used to identify the state in experiments. Using real-space dynamical mean field theory (DMFT), we compute the phase diagram of a trapped, spin-polarized Fermi gas in a dimensional crossover from a 1D to a 3D optical lattice. We find that the FFLO state is realized in a broad region of parameters throughout the crossover while the shell structure of the Fermi gas preceding the transition to the full FFLO state shows a strong dependence on the dimensionality. Finally, we utilize the cluster DMFT method to show that the FFLO state is stable against non-local quantum fluctuations even though these fluctuations do affect the critical temperature of the state.
Ultracold atomic gases have emerged as an ideal laboratory system to emulate many-body physics in an unprecedentedly controllable manner. Numerous many-body quantum states and phases have been experimentally explored and characterized using the ultracold atomic gases, offering new insights into many exciting physics ranging from condensed matters to cosmology. In this thesis, we will present a systematic numerical study of a novel experimental system, population imbalanced two-component ultracold Fermi gases. We explore the phase diagram of this system in both 3D and 1D especially focusing on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which is characterized by a spatially oscillating order parameter. In 3D, we solve for the stationary states of trapped imbalanced Fermi gases in a wide range of parameter space with a home-made parallel eigen-solver for Bogoliubov-de Gennes (BdG) equations. Our results show that there exists a metastable state with a FFLO type oscillating order parameter. In 1D, we simulate the dynamical expansion of the population imbalanced Fermi gases from the trap. A numerically quasi-exact scheme, time-evolving block decimation (TEBD), is introduced for the comparative studies with the solution of the time-dependent BdG equation. Our results predict that the existence of FFLO states will leave conspicuous signatures in the density profiles during the expansion. For further understanding of the interplay between the population imbalance and two-body pairing interaction between two spin components, we also study the spin transport properties through trapped ultracold Fermi gases. The preliminary results will be discussed.
This work considers the theory of ultracold Fermi gases. We study the spin-asymmetric Josephson effect where the spin components of a Cooper pair feel spin-dependent potentials during the tunneling process and as a result oscillate at the same Josephson frequency but with different amplitudes. This contrasts the conventional interpretation of the Josephson effect in which the Cooper-paired spins 'tunnel together'. Here, we propose a new experimental arrangement to detect the yet-unobserved spin-asymmetric Josephson effect. We investigate two-component fermions in a one-dimensional spin-dependent optical superlattice described by a Fermi-Hubbard Hamiltonian and simulate the dynamics of the set-up with the essentially exact time-evolving block decimation (TEBD) numerical method. We demonstrate that the characteristics of the spin-asymmetric Josephson effect, frequency-synchronized particle number oscillations with spin-asymmetric critical currents, are present in the system. We show that the Josephson frequency depends only on the sum of the spin-dependent potential offsets between two adjacent sites in the super-lattice. We further exhibit that significant asymmetries of over 10% in the critical currents of the spin components are feasible. We also evince that the properties of the particle currents in the super-lattice system agree with the analytical results given by a Hubbard dimer model consisting of only one unit cell of the super-lattice in the strongly interacting limit.
Ultracold gases are of great interest in modern physics. The main reason is that in the systems of ultracold gases the parameters can be easily tuned, thus they can be used as a testing ground for various quantum many-body theories. Interesting macroscopic quantum effects have been observed in the ultracold gas systems, for instance Bose-Einstein condensation. In this thesis, theoretical knowledge of ultracold gases is extended. A summary of the methods used in this thesis is given, including a detailed description of the density response theory and the time-evolving block decimation (TEBD) algorithm. Collective excitations of an ultracold gas in a three-dimensional (3D) spherically symmetric trap are studied in detail in publications II and III. As a result, several collective modes are discovered such as a low energy Higgs-type mode, a second sound-like mode, and a strong mode resembling the Leggett mode. Using the TEBD algorithm, physics of a polaron in a one-dimensional (1D) lattice, and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in 1D are studied in publications IV and I, respectively. In publication I a method to detect the FFLO phase is suggested, namely by the observation of the change in the double occupancy after a lattice depth modulation. Publication IV compares a variational ansatz and the TEBD simulations and finds an excellent agreement, indicating that the variational ansatz can be used to describe the system for a certain range of interactions.
Expansion dynamics of interacting fermions in a lattice is simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and nonpaired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.