arXiv subjects

Brendan C. Mulkerin

Publications and source records attributed to Brendan C. Mulkerin.

30 records · Page 2Linked to original sources

arXiv2019

Leggett mode in a two-component Fermi gas with dipolar interactions

We develop an effective field theory to understand collective modes of a three-dimensional two-component Fermi superfluid with dipolar inter-particle interactions, which are modeled by an idealized separable potential. We first examine the phase transition of the system at zero temperature, as the fermionic superfluidity is known to be characterized by two competing order parameters. We find that for strong interactions there exists a regime where the two order parameters are out-of-phase and coupled, giving rise to an undamped massive Leggett mode. This is in addition to the well-known gapless phonon mode. We show that the Leggett mode can be seen in the spectral function of the in-medium Cooper pairs, and in principle could be measured through Bragg spectroscopy.

cond-mat.quant-gas↗

arXiv2018

Reduced quantum anomaly in a quasi-2D Fermi superfluid: The significance of the confinement-induced effective range of interactions

A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale invariant value $ω_{B}=2ω_{\perp}$, where $ω_{\perp}$ is the trapping frequency. The predicted maximum quantum anomaly ($\sim10\%$) has not been confirmed in experiments. Here, we theoretically investigate the zero-temperature density equation of state and the breathing mode frequency of an interacting Fermi superfluid at the dimensional crossover from three to two dimensions. We find that the simple model of a 2D Fermi gas with a single $s$-wave scattering length is not adequate to describe the experiments in the 2D limit, as commonly believed. A more complete description of quasi-2D leads to a much weaker quantum anomaly, consistent with the experimental observations. We clarify that the reduced quantum anomaly is due to the significant confinement-induced effective range of interactions, which is overlooked in previous theoretical and experimental studies.

cond-mat.quant-gas↗

arXiv2018

Quantum fluctuations of a resonantly interacting $p$-wave Fermi superfluid in two dimensions

Using the Gaussian pair fluctuation theory, we investigate quantum fluctuations of a strongly interacting two-dimensional chiral \textit{p}-wave Fermi superfluid at the transition from a Bose-Einstein condensate (BEC) to a topologically non-trivial Bardeen-Cooper-Schrieffer (BCS) superfluid. Near the topological phase transition at zero chemical potential, $μ=0$, we observe that quantum fluctuations strongly renormalize the zero-temperature equations of state, sound velocity, pair-breaking velocity, and Berezinskii-Kosterlitz-Thouless (BKT) critical temperature of the Fermi superfluid, all of which can be non-analytic functions of the interaction strength. The indication of non-analyticity is particularly evident in the BKT critical temperature, which also exhibits a pronounced peak near the topological phase transition. Across the transition and towards the BEC limit we find that the system quickly becomes a trivial interacting Bose liquid, whose properties are less dependent on the interparticle interaction. The qualitative behavior of composite bosons in the BEC limit remains to be understood.

cond-mat.quant-gas↗

arXiv2018

Breathing mode frequency of a strongly interacting Fermi gas across the 2D-3D dimensional crossover

We address the interplay between dimension and quantum anomaly on the breathing mode frequency of a strongly interacting Fermi gas harmonically trapped at zero temperature. Using a beyond mean-field, Gaussian pair fluctuation theory, we employ periodic boundary conditions to simulate the dimensionality of the system and impose a local density approximation, with two different schemes, to model different trapping potentials in the tightly-confined axial direction. By using a sum-rule approach, we compute the breathing mode frequency associated with a small variation of the trapping frequency along the weakly-confined transverse direction, and describe its behavior as functions of the dimensionality, from two- to three-dimensions, and of the interaction strength. We compare our predictions with previous calculations on the two-dimensional breathing mode anomaly and discuss their possible observation in ultracold Fermi gases of $^{6}$Li and $^{40}$K atoms.

cond-mat.quant-gas↗

arXiv2018

Ultra-cold Collisions between Spin-Orbit-Coupled Dipoles: General Formalism and Universality

A theoretical study of the low-energy scattering properties of two aligned identical bosonic and fermionic dipoles in the presence of isotropic spin-orbit coupling (SOC) is presented. A general treatment of particles with arbitrary (pseudo-) spin is given in the framework of multi-channel scattering. At ultracold temperatures and away from shape resonances or closed-channel dominated resonances, the cross-section can be well described within the Born approximation to within corrections due to the s-wave scattering. We compare our findings with numerical calculations and find excellent agreement.

cond-mat.quant-gas↗

arXiv2017

Collective modes of a two-dimensional Fermi gas at finite temperature

In this work we examine the breathing mode of a strongly interacting two-dimensional Fermi gas and the role of temperature on the anomalous breaking of scale invariance. By calculating the equation of state with different many-body $T$-matrix theories and the virial expansion approach, we obtain a hydrodynamic equation of the harmonically trapped Fermi gas (with trapping frequency $ω_{0}$) through the local density approximation. By solving the hydrodynamic equation we determine the breathing mode frequencies as functions of interaction strength and temperature. We find that the breathing mode anomaly depends sensitively on both interaction strength and temperature. In particular, in the strongly interacting regime we predict a significant down-shift of the breathing mode frequency, below the scale invariant value of $2ω_{0}$ for temperatures of order the Fermi temperature.

cond-mat.quant-gas↗

arXiv2017

Attractive Fermi polarons at nonzero temperature with finite impurityconcentration

We theoretically investigate how quasi-particle properties of an attractive Fermi polaron are affected by nonzero temperature and finite impurity concentration. By applying both non-self-consistent and self-consistent many-body $T$-matrix theories, we calculate the polaron energy (including decay rate), effective mass, and residue, as functions of temperature and impurity concentration. The temperature and concentration dependences are weak on the BCS side with a negative impurity-medium scattering length. Toward the strong attraction regime across the unitary limit, we find sizable dependences. In particular, with increasing temperature the effective mass quickly approaches the bare mass and the residue is significantly enhanced. At the temperature $T\sim0.1T_{F}$, where $T_{F}$ is the Fermi temperature of the background Fermi sea, the residual polaron-polaron interaction seems to become attractive. This leads to a notable down-shift in the polaron energy. We show that, by taking into account the temperature and impurity concentration effects, the measured polaron energy in the first Fermi polaron experiment {[}A. Schirotzek \textit{et al.}, Phys. Rev. Lett. \textbf{102}, 230402 (2009){]} can be better theoretically explained.

cond-mat.quant-gas↗

arXiv2017

Superfluid density and critical velocity near the fermionic Berezinskii-Kosterlitz-Thouless transition

We theoretically investigate superfluidity in a strongly interacting Fermi gas confined to two dimensions at finite temperature. Using a Gaussian pair fluctuation theory in the superfluid phase, we calculate the superfluid density and determine the critical temperature and chemical potential at the Berezinskii-Kosterlitz-Thouless transition. We propose that the transition can be unambiguously demonstrated in cold-atom experiments by stirring the superfluid Fermi gas using a red detuned laser beam, to identify the characteristic jump in the local Landau critical velocity at the superfluid-normal interface, as the laser beam moves across the cloud.

cond-mat.quant-gas↗

arXiv2017

Dimensional crossover in a strongly interacting ultracold atomic Fermi gas

We theoretically explore the crossover from three dimensions (3D) to two (2D) in a strongly interacting atomic Fermi superfluid through confining the transverse spatial dimension. Using the gaussian pair fluctuation theory, we determine the zero-temperature equation of state and Landau critical velocity as functions of the spatial extent of the transverse dimension and interaction strength. In the presence of strong interactions, we map out a dimensional crossover diagram from the location of maximum critical velocity, which exhibits distinct dependence on the transverse dimension from 2D to quasi-2D, and to 3D. We calculate the dynamic structure factor to characterize the low-energy excitations of the system and propose that the intermediate quasi-2D regime can be experimentally probed using Bragg spectroscopy.

cond-mat.quant-gas↗

arXiv2016

Beyond Gaussian pair fluctuation theory for strongly interacting Fermi gases

Interacting Fermi systems in the strongly correlated regime play a fundamental role in many areas of physics and are of particular interest to the condensed matter community. Though weakly inter- acting fermions are understood, strongly correlated fermions are difficult to describe theoretically as there is no small interaction parameter to expand about. Existing strong coupling theories rely heavily on the so-called many-body T-matrix approximation that sums ladder-type Feynman diagrams. Here, by acknowledging the fact that the effective interparticle interaction (i.e., the vertex function) becomes smaller above three dimensions, we propose an alternative way to reorganize Feynman diagrams and develop a theoretical framework for interacting Fermi gases beyond the ladder approximation. As an application, we solve the equation of state for three- and two-dimensional strongly interacting fermions and find excellent agreement with experimental [Science 335, 563 (2012)] and other theoretical results above the temperature 0.5TF .

cond-mat.quant-gas↗

arXiv2016

Comparison of strong-coupling theories for a two-dimensional Fermi gas

Understanding the formation of Cooper pairs and the resulting thermodynamic properties of a low-dimensional Fermi gas is an important area of research, elucidating our understanding of high temperature superconductors. In lower dimensions quantum fluctuations are expected to play an increasingly important role and the reliability of strong-coupling theories becomes questionable. Here, we present a comparison of recent thermodynamic measurements and theoretical predictions from different many-body $T$-matrix theories for a two-dimensional strongly interacting Fermi gas in the normal state. We find that the fully self-consistent $T$-matrix theory provides the best description of the experimental data over a wide range of temperatures and interatomic interactions. Our comparison reveals the crucial role played by the interactions between Cooper pairs and suggests that the future development of a quantitative strong-coupling theory for two-dimensional Fermi superfluids must explicitly take into account the diagrams that are responsible for pair-pair interactions.

cond-mat.quant-gas↗

arXiv2011

Determining the validity of solutions of the meanfield Bogoliubov-de Gennes equation

We provide a general methodology to directly determine the validity of the meanfield Bogoliubov-de Gennes equation. In particular we apply this methodology to the case of two component interacting ultracold Fermi gases. As an example, we consider the case of population imbalance, between the two components, in the strongly attractive interacting regime, where meanfield results predict Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. For these states we find at finite temperatures that the assumptions used to derive the Bogoliubov-de Gennes equation are invalid.

quant-ph↗