10 research outputs found
Quantum phase transitions and Berezinskii-Kosterlitz-Thouless temperature in a two-dimensional spin-orbit-coupled Fermi gas
We study the effect of spin-orbit coupling on both the zero-temperature and
non-zero temperature behavior of a two-dimensional (2D) Fermi gas. We include a
generic combination of Rashba and Dresselhaus terms into the system
Hamiltonian, which allows us to study both the experimentally relevant
equal-Rashba-Dresselhaus (ERD) limit and the Rashba-only (RO) limit. At zero
temperature, we derive the phase diagram as a function of the two-body binding
energy and Zeeman field. In the ERD case, this phase diagram reveals several
topologically distinct uniform superfluid phases, classified according to the
nodal structure of the quasiparticle excitation energies. Furthermore, we use a
momentum dependent SU(2)-rotation to transform the system into a generalized
helicity basis, revealing that spin-orbit coupling induces a triplet pairing
component of the order parameter. At non-zero temperature, we study the
Berezinskii-Kosterlitz-Thouless (BKT) phase transition by including phase
fluctuations of the order parameter up to second order. We show that the
superfluid density becomes anisotropic due to the presence of spin-orbit
coupling (except in the RO case). This leads both to elliptic vortices and
antivortices, and to anisotropic sound velocities. The latter prove to be
sensitive to quantum phase transitions between topologically distinct phases.
We show further that at a fixed non-zero Zeeman field, the BKT critical
temperature is increased by the presence of ERD spin-orbit coupling.
Subsequently, we demonstrate that the Clogston limit becomes infinite:
remains non-zero at all finite values of the Zeeman field. We
conclude by extending the quantum phase transition lines to non-zero
temperature, using the nodal structure of the quasiparticle spectrum, thus
connecting the BKT critical temperature with the zero-temperature results.Comment: 17 pages, 7 figure
Effects of spin-orbit coupling on the Berezinskii-Kosterlitz-Thouless transition and the vortex-antivortex structure in two-dimensional Fermi gases
We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a
two-dimensional (2D) Fermi gas with spin-orbit coupling (SOC), as a function of
the two-body binding energy and a perpendicular Zeeman field. By including a
generic form of the SOC, as a function of Rashba and Dresselhaus terms, we
study the evolution between the experimentally relevant equal
Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in
the ERD case, at fixed non-zero Zeeman field, the BKT transition temperature
is increased by the effect of SOC for all values of the binding
energy. We also find a significant increase in the value of the Clogston limit
compared to the case without SOC. Furthermore, we demonstrate that the
superfluid density tensor becomes anisotropic (except in the RO case), leading
to an anisotropic phase-fluctuation action that describes elliptic vortices and
antivortices, which become circular in the RO limit. This deformation
constitutes an important experimental signature for superfluidity in a 2D Fermi
gas with ERD SOC. Finally, we show that the anisotropic sound velocities
exhibit anomalies at low temperatures, in the vicinity of quantum phase
transitions between topologically distinct uniform superfluid phases.Comment: 5 pages, 3 figure
Controlling the pair momentum of the FFLO state in a 3D Fermi gas through a 1D periodic potential
The question whether a spin-imbalanced Fermi gas can accommodate the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state has been the subject of intense
study. This state, in which Cooper pairs obtain a nonzero momentum, has
hitherto eluded experimental observation. Recently, we demonstrated that the
FFLO state can be stabilized in a 3D Fermi gas, by adding a 1D periodic
potential. Until now it was assumed that the FFLO wave vector always lies
parallel to this periodic potential (FFLO-P). In this contribution we show
that, surprisingly, the FFLO wave vector can also lie skewed with respect to
the potential (FFLO-S). Starting from the partition sum, the saddle-point free
energy of the system is derived within the path-integral formalism. Minimizing
this free energy allows us to study the different competing ground states of
the system. To qualitatively understand the underlying pairing mechanism, we
visualize the Fermi surfaces of the spin up and spin down particles. From this
visualization, we find that tilting the FFLO wave vector with respect to the
direction of the periodic potential, can result in a larger overlap between the
pairing bands of both spin species. This skewed FFLO state can provide an
additional experimental signature for observing FFLO superfluidity in a 3D
Fermi gas.Comment: 19 pages, 3 figure
Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures
The spectra of low-lying pair excitations for an imbalanced two-component
superfluid Fermi gas are analytically derived within the path-integral
formalism taking into account Gaussian fluctuations about the saddle point. The
spectra are obtained for nonzero temperatures, both with and without imbalance,
and for arbitrary interaction strength. On the basis of the pair excitation
spectrum, we have calculated the thermodynamic parameters of state of cold
fermions and the first and second sound velocities. The parameters of pair
excitations show a remarkable agreement with the Monte Carlo data and with
experiment.Comment: 14 pages, 5 figure
Path integral approach to Asian options in the Black-Scholes model
We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.
Effect of phase fluctuations on the Fulde-Ferrell-Larkin-Ovchinnikov state in a three-dimensional Fermi gas
Abstract: In ultracold Fermi gases, the effect of spin imbalance on superfluidity has been the subject of intense study. One of the reasons for this is that spin imbalance frustrates the Bardeen-Cooper-Schrieffer (BCS) superfluid pairing mechanism, in which fermions in different spin states combine into Cooper pairs with zero momentum. In 1964, it was proposed that an exotic superfluid state called the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the Cooper pairs have nonzero momentum, could exist in a spin-imbalanced Fermi gas. At the saddle-point (mean-field) level, it has been shown that the FFLO state only occupies a very small sliver in the ground-state phase diagram of a three-dimensional (3D) Fermi gas. However, a question that remains to be investigated is as follows: What is the influence of phase fluctuations on the FFLO state? In this work, we show that phase fluctuations only lead to relatively small quantitative corrections to the presence of the FFLO state in the saddle-point phase diagram of a 3D spin-imbalanced Fermi gas. Starting from the partition function of the system, we calculate the effective action within the path-integral adiabatic approximation. The action is then expanded up to second order in the fluctuation field around the saddle point, leading to the fluctuation free energy. Using this free energy, we calculate corrections due to phase fluctuations to the BCS-FFLO transition in the saddle-point phase diagram. At temperatures at which the FFLO state exists, we find only small corrections to the size of the FFLO area. Our results suggest that fluctuations of the phase of the FFLO order parameter, which can be interpreted as an oscillation of its momentum vector, do not cause an instability of the FFLO state with respect to the BCS state