arXiv subjects

Xia-Ji Liu

Publications and source records attributed to Xia-Ji Liu.

At least 37 records · Page 2Linked to original sources

arXiv2023

Spectral function of Fermi polarons at finite temperature from a self-consistent many-body $T$-matrix approach in real frequency

We theoretically examine the finite-temperature spectral function of Fermi polarons in three dimensions, by using a self-consistent many-body $T$-matrix theory in real frequency. In comparison with the previous results from a non-self-consistent many-body $T$-matrix approach, we show that the treatment of self-consistency in the impurity Green function leads to notable changes in almost all the dynamical quantities, including the vertex function, impurity self-energy and spectral function. Eventually, it gives rise to quantitatively different predictions for the measurable radio-frequency spectrum and Raman spectrum at finite temperature. Using the recent spectroscopic measurements as a benchmark, we find that the self-consistent many-body $T$-matrix theory somehow provides a better explanation for the experimental data. The notable difference in the predictions from the non-self-consistent and self-consistent theories suggests that more accurate theoretical descriptions are needed, in order to fully account for the current spectroscopic observations on Fermi polarons.

cond-mat.quant-gas↗

arXiv2023

Thermally stable p-wave repulsive Fermi polaron without a two-body bound state

We theoretically investigate the polaron physics of an impurity immersed in a two-dimensional Fermi sea, interacting via a p-wave interaction at finite temperature. In the unitary limit with a divergent scattering area, we find a well-defined repulsive Fermi polaron at short interaction range, which shows a remarkable thermal stability with increasing temperature. The appearance of such a stable repulsive Fermi polaron in the resonantly interacting limit can be attributed to the existence of a quasi-bound dressed molecule state hidden in the two-particle continuum, although there is no bound state in the two-particle limit. We show that the repulsive Fermi polaron disappears when the interaction range increases or when the scattering area is tuned to the weakly-interacting regime. The large interaction range and small scattering area instead stabilize attractive Fermi polarons.

cond-mat.quant-gas↗

arXiv2022

Raman spectroscopy of Fermi polarons

By using a non-self-consistent many-body $T$-matrix theory, we calculate the finite-temperature Raman spectroscopy of a mobile impurity immersed in a Fermi bath in three dimensions. The dependences of the Raman spectrum on the transferred momentum, temperature, and impurity-bath interaction are discussed in detail. We confirm that the peak in the Raman spectrum shows a weaker dependence on the impurity concentration than that in the radio-frequency spectroscopy, due to the nonzero transferred momentum, as anticipated. We compare our theoretical prediction with the recent measurement by Gal Ness \textsl{et al.} in Physical Review X \textbf{10}, 041019 (2020) without any adjustable parameters. At weak coupling, we find a good quantitative agreement. However, close to the Feshbach resonance the agreement becomes worse. At strong coupling, we find that an unrealistic Fermi bath temperature might be needed, in order to account for the experimental data.

cond-mat.quant-gas↗

arXiv2022

BCS-BEC crossover in a quasi-two-dimensional Fermi superfluid

We study the crossover from the Bardeen-Cooper-Shrieffer (BCS) regime to the Bose-Einstein-condensation (BEC) regime in a quasi-two-dimensional quantum gas of ultracold fermionic atoms. Using an effective two-dimensional Hamiltonian with renormalized interactions between atoms and dressed molecules within a Gaussian pair fluctuation theory, we investigate how Fermi superfluidity is affected by reduced dimensionality at zero temperature in a wide range of crossover. We observe that the order parameter and pair size show universal relations with the chemical potential on the BCS side, irrespective of dimensionality. However, such universal dependences break down towards the BEC limit with increasing interaction strength. This results reveal the notable effect of reduced dimenionality on pairing physics, which can also be observed in the sound velocity and convexity parameter of the Goldstone mode. We compare our results with the latest experiments in both ${}^{6}$Li atomic gases and layered nitrides LixZrNCl and find good agreements.

cond-mat.quant-gas↗

arXiv2022

Two-dimensional coherent spectroscopy of trion-polaritons and exciton-polaritons in atomically thin transition metal dichalcogenides

We present a microscopic many-body calculation of the nonlinear two-dimensional coherent spectroscopy (2DCS) of trion-polaritons and exciton-polaritons in charge-tunable transition-metal-dichalcogenides monolayers placed in an optical microcavity. The charge tunability leads to an electron gas with nonzero density that brings brightness to the trion - a polaron quasiparticle formed by an exciton with a nonzero residue bounded to the electron gas. As a result, a trion-polariton is created under strong light-matter coupling, as observed in the recent experiment by Sidler \textit{et al.} {[}Nat. Phys. \textbf{13}, 255 (2017){]}. We analyze in detail the structure of trion-polaritons, by solving an extended Chevy ansatz for the trion quasiparticle wave-function. We confirm that the effective light-matter coupling for trion-polaritons is determined by the residue of the trion quasiparticle. The solution of the full many-body polaron states within Chevy ansatz enables us to microscopically calculate the nonlinear 2DCS spectrum of both trion-polaritons and exciton-polaritons. We predict the existence of three kinds of off-diagonal cross-peaks in the 2DCS spectrum, as an indication of the coherence among the different branches of trion-polaritons and exciton-polaritons. Due to the sensitivity of 2DCS spectrum to quasiparticle interactions, our work provides a good starting point to explore the strong nonlinearity exhibited by trion-polaritons in some recent exciton-polariton experiments.

cond-mat.quant-gas↗

arXiv2022

Microscopic many-body theory of two-dimensional coherent spectroscopy of excitons and trions in atomically thin transition metal dichalcogenides

We present a microscopic many-body theory of the recently measured two-dimensional coherent spectroscopy (2DCS) of excitons and trions in monolayer MoSe$_{2}$ materials {[}K. Hao \textit{et al.}, Nano Lett. \textbf{16}, 5109 (2016){]}, where excitons and trions can be well interpreted as repulsive and attractive polarons, respectively, in the dilute limit of exciton density. We derive a simple relation for the 2DCS spectrum in terms of a modified, mixing time-dependent polaron Green function, which is valid in the single exciton limit. Our simulated spectra are in excellent qualitative agreement with experiments without introducing any phenomenological parameters such as decoherence rates. In particular, quantum beats between the off-diagonal crosspeaks in the experimental 2DCS spectra are well reproduced. Our work, therefore, clarifies the microscopic principle that underlies the observed optical signals of exciton-trion coherence. We find that there are two quantitative discrepancies between theory and experiment: the smaller than expected crosspeak strength and the slightly unsynchronized quantum beats at different crosspeaks. Tentatively, we attribute these residual discrepancies to the finite exciton density and the resultant polaron-polaron interaction, which is not taken into account in our theory.

cond-mat.mes-hall↗

arXiv2022

Two-dimensional spectroscopic diagnosis of quantum coherence in Fermi polarons

We present a full microscopic many-body calculation of a recently-proposed nonlinear two-dimensional spectroscopy for Fermi polarons, and show that the quantum coherence between the attractive and repulsive polarons, which has never been experimentally examined, can be unambiguously revealed via quantum beats at the two off-diagonal crosspeaks in the two-dimensional spectrum. We predict that particle-hole excitations make the two crosspeaks asymmetric and lead to an additional side peak near the diagonal repulsive polaron peak. Our simulated spectra can be readily examined in future cold-atom experiments, where the two-dimensional spectroscopy is to be implemented by using a Ramsey interference sequence of rf pulses in the time domain. Our results also provide a first-principle understanding of the recent two-dimensional coherent spectroscopy of interacting excitons and trions in doped monolayer transition metal dichalcogenides.

cond-mat.quant-gas↗

arXiv2022

Second sound with ultracold atoms: A brief historical account

We briefly review the research on second sound in ultracold atomic physics, with emphasis on strongly interacting unitary Fermi gases with infinitely large $s$-wave scattering length. Second sound is a smoking-gun feature of superfluidity in any quantum superfluids. The observation and characterization of second sound in ultracold quantum gases has been a long-standing challenge, and in recent years there are rapid developments due to the experimental realization of a uniform box-trap potential. The purpose of this review is to present a brief historical account of the key research activities on second sound over the past two decades. We summarize the initial theoretical works that reveal the characteristics of second sound in a unitary Fermi gas, and introduce its first observation in a highly elongated harmonic trap. We then discuss the most recent measurement on second sound attenuation in a uniform setup, which may open a new era to understand quantum transport near quantum criticality in the strongly interacting regime. The observation of second sound in homogeneous weakly interacting Bose condensates in both two and three dimensions are also briefly introduced.

cond-mat.quant-gas↗

arXiv2022

Superfluidity of a Raman spin-orbit-coupled Bose gas at finite temperature

We investigate the superfluidity of a three-dimensional weakly interacting Bose gas with a one-dimensional Raman-type spin-orbit coupling at both zero and finite temperatures. Using the imaginary-time Green's function within the Bogoliubov approximation, we explicitly derive analytic expressions of the current-current response functions in the plane-wave and zero-momentum phases, from which we extract the superfluid density in the limits of long wavelength and zero frequency. At zero temperature, we check that the resultant superfluid density agrees exactly with our previous analytic prediction obtained from a phase-twist approach. Both results also satisfy a generalized Josephson relation in the presence of spin-orbit coupling. At finite temperature, we find a significant non-monotonic temperature dependence of superfluid density near the transition from the plane-wave phase to the zero-momentum phase. We show that this non-trivial behavior might be understood from the sound velocity, which has a similar temperature dependence. The non-monotonic temperature dependence is also shared by Landau critical velocity, above which the spin-orbit-coupled Bose gas loses its superfluidity. Our results would be useful for further theoretical and experimental studies of superfluidity in exotic spin-orbit coupled quantum gases.

cond-mat.quant-gas↗

arXiv2022

Crossover polarons in a strongly interacting Fermi superfluid

We investigate the zero-temperature quasiparticle properties of a mobile impurity immersed in a strongly interacting Fermi superfluid at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen--Cooper--Schrieffer (BCS) superfluid, by using a many-body $T$-matrix approach that excludes Efimov trimer bound states. Termed BEC-BCS crossover polaron, or crossover polaron in short, this quasiparticle couples to elementary excitations of a many-body background and therefore could provide a useful probe of the underlying strongly interacting Fermi superfluid. Due to the existence of a significant pairing gap $Δ$, we find that the repulsive polaron branch becomes less well-defined. In contrast, the attractive polaron branch is protected by the pairing gap and becomes more robust at finite momentum. It remains as a delta-function peak in the impurity spectral function below a threshold $2Δ$. Above the threshold, the attractive polaron enters the particle-hole continuum and starts to get damped. We predict the polaron energy, residue and effective mass for realistic Bose-Fermi mixtures, where the minority bosonic atoms play the role of impurity. These results are practically useful for future cold-atom experiments on crossover polarons.

cond-mat.quant-gas↗

arXiv2022

Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: formalism and applications

We investigate the system of a heavy impurity embedded in a paired two-component Fermi gas at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen--Cooper--Schrieffer (BCS) superfluid via an extension of the functional determinant approach (FDA). FDA is an exact numerical approach applied to study manifestations of Anderson\textquoteright s orthogonality catastrophe (OC) in the system of a static impurity immersed in an ideal Fermi gas. Here, we extend the FDA to a strongly correlated superfluid background described by a BCS mean-field wavefunction. In contrast to the ideal Fermi gas case, the pairing gap in the BCS superfluid prevents the OC and leads to genuine polaron signals in the spectrum. Thus, our exactly solvable model can provide a deeper understanding of polaron physics. In addition, we find that the polaron spectrum can be used to measure the superfluid pairing gap, and in the case of a magnetic impurity, the energy of the sub-gap Yu-Shiba-Rusinov (YSR) bound state. Our theoretical predictions can be examined with state-of-art cold-atom experiments.

cond-mat.quant-gas↗

arXiv2022

Pseudopotentials for Two-dimentional Ultracold Scattering in the Presence of Synthetic Spin-orbit-coupling

We derive a pseudopotential in two dimensions (2D) with the presence of a 2D Rashba spin-orbit-coupling (SOC), following the same spirit of frame transformation in {[}Phys. Rev. A 95, 020702(R) (2017){]}. The frame transformation correctly describes the non-trivial phase accumulation and partial wave couplings due to the presence of SOC and gives rise to a different pseudopotential than the free-space one, even when the length scale of SOC is significantly larger than the two-body potential range. As an application, we apply our pseudopotential with the Lippmann-Schwinger equation to obtain an analytical scattering matrix. To demonstrate the validity, we compare our results with a numerical scattering calculation of finite-range potential and show perfect agreement over a wide range of scattering energy and SOC strength. Our results also indicate that the differences between our pseudopotential and the original free-space pseudopotential are essential to reproduce scattering observables correctly.

cond-mat.quant-gas↗

arXiv2022

Photo-excitation measurement of Tan's contact for a strongly interacting Fermi gas

We derive theoretically an exact relation between Tan's universal contact and the photo-excitation rate of a strongly interacting Fermi gas, in the case of optically transferring fermionic pairs to a more tightly bound molecular state. Our deviation generalizes the relation between Tan's contact and the closed-channel molecular fraction found earlier by Werner, Tarruell and Castin in Eur. Phys. J. B \textbf{68}, 401 (2009). We use the relation to understand the recent low-temperature photo-excitation measurement in a strongly interacting $^{6}$Li Fermi gas {[}Liu \textit{et al.}, arXiv:1903.12321{]} and show that there is a reasonable agreement between theory and experiment close to the unitary limit. We propose that our relation can be applied to accurately measure Tan's contact coefficient at finite temperature in future experiments.

cond-mat.quant-gas↗

arXiv2022

Exact quasiparticle properties of a heavy polaron in BCS Fermi superfluids

We present the Ramsey response and radio-frequency spectroscopy of a heavy impurity immersed in an interacting Fermi superfluid, using exact functional determinant approach. We describe the Fermi superfluid through the conventional Bardeen-Cooper-Schrieffer theory and investigate the role of the pairing gap on quasiparticle properties revealed by the two spectroscopies. The energy cost for pair breaking prevents Anderson\textquoteright s orthogonality catastrophe that occurs in a non-interacting Fermi gas and allows the existence of polaron quasiparticles in the exactly solvable heavy impurity limit. Hence, we rigorously confirm the remarkable features such as dark continuum, molecule-hole continuum and repulsive polaron. For a magnetic impurity scattering at finite temperature, we predict additional resonances related to the sub-gap Yu-Shiba-Rusinov bound state, whose positions can be used to measure the superfluid pairing gap. For a non-magnetic scattering at zero temperature, we surprisingly find undamped repulsive polarons. These exact results might be readily observed in quantum gas experiments with Bose-Fermi mixtures that have a large-mass ratio.

cond-mat.quant-gas↗

arXiv2022

Fermi polarons at finite temperature: Spectral function and rf-spectroscopy

We present a systematic study of a mobile impurity immersed in a three-dimensional Fermi sea of fermions at finite temperature, by using the standard non-self-consistent many-body $T$-matrix theory that is equivalent to a finite-temperature variational approach with the inclusion of one-particle-hole excitation. The impurity spectral function is determined in the real-frequency domain, avoiding any potential errors due to the numerical analytic continuation in previous $T$-matrix calculations and the small spectral broadening parameter used in variational calculations. In the weak-coupling limit, we find that the quasiparticle decay rate of both attractive and repulsive polarons does not increase significantly with increasing temperature, and therefore Fermi polarons may remain well-defined far above Fermi degeneracy. In contrast, near the unitary limit with strong coupling, the decay rate of Fermi polarons rapidly increase and the quasiparticle picture breaks down close to the Fermi temperature. We analyze in detail the recent ejection and injection radio-frequency (rf) spectroscopy measurements, performed at Massachusetts Institute of Technology (MIT) and at European Laboratory for Non-Linear Spectroscopy (LENS), respectively. We show that the momentum average of the spectral function, which is necessary to account for the observed rf-spectroscopy, has a sizable contribution to the width of the quasiparticle peak in spectroscopy. As a result, the measured decay rate of Fermi polarons could be significantly larger than the calculated quasiparticle decay rate at zero momentum. By take this crucial contribution into account, we find that there is a reasonable agreement between theory and experiment for the lifetime of Fermi polarons in the strong-coupling regime, as long as they remain well-defined.

cond-mat.quant-gas↗

arXiv2022

Beyond Gaussian pair fluctuation theory for strongly interacting Fermi gases II: The broken-symmetry phase

We theoretically study the thermodynamic properties of a strongly interacting Fermi gas at the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC), by applying a recently outlined strong-coupling theory that includes pair fluctuations beyond the commonly-used many-body $T$-matrix or ladder approximation at the Gaussian level. The beyond Gaussian pair fluctuation (GPF) theory always respects the exact thermodynamic relations and recovers the Bogoliubov theory of molecules in the BEC limit with a nearly correct molecule-molecule scattering length. We show that the beyond-GPF theory predicts quantitatively accurate ground-state properties at the BEC-BCS crossover, in good agreement with the recent measurement by Horikoshi \textit{et al.} in Phys. Rev. X \textbf{7}, 041004 (2017). In the unitary limit with infinitely large $s$-wave scattering length, the beyond-GPF theory predicts a reliable universal energy equation of state up to 0.6$T_c$, where $T_c$ is the superfluid transition temperature at unitarity. The theory predicts a Bertsch parameter $ξ\simeq 0.365$ at zero temperature, in good agreement with the latest quantum Monte Carlo result $ξ= 0.367(7)$ and the latest experimental measurement $ξ= 0.367(9)$. We attribute the excellent and wide applicability of the beyond-GPF theory in the broken-symmetry phase to the reasonable re-summation of Feynman diagrams following a dimensional $ε$-expansion analysis near four dimensions ($d=4-ε$), which gives rise to accurate predictions at the second order $\mathcal{O}(ε^2)$. Our work indicates the possibility of further improving the strong-coupling theory of strongly interacting fermions based on the systematic inclusion of large-loop Feynman diagrams at higher orders $\mathcal{O}(ε^n)$ with $n\ge 3$.

cond-mat.quant-gas↗

arXiv2021

First-order Bose-Einstein condensation with three-body interacting bosons

Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here, we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an $s$-wave scattering length $a<0$ and a three-body scattering hypervolume $D>0$. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquid-like quantum droplet to a normal gas, and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurred later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tri-critical point, where the three phases - quantum droplet, superfluid gas and normal gas - meet together. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.

cond-mat.quant-gas↗

arXiv2021

Anderson localization transition in a robust $\mathcal{PT}$-symmetric phase of a generalized Aubry-Andre model

We study a generalized Aubry-Andre model that obeys $\mathcal{PT}$-symmetry. We observe a robust $\mathcal{PT}$-symmetric phase with respect to system size and disorder strength, where all eigenvalues are real despite the Hamiltonian being non-hermitian. This robust $\mathcal{PT}$-symmetric phase can support an Anderson localization transition, giving a rich phase diagram as a result of the interplay between disorder and $\mathcal{PT}$-symmetry. Our model provides a perfect platform to study disorder-driven localization phenomena in a $\mathcal{PT}$-symmetric system.

cond-mat.dis-nn↗