Session E08: Quantum Gases in Low Dimensions I

Spin-charge separation in a 1D Fermi gas with tunable interactions

Ultracold atoms confined in optical lattices are a powerful tool for quantum simulation of complex many-body systems. We confine spin-1/2 atomic fermions (⁶Li) to one dimension and realize the Yang-Gaudin model, the low-energy behavior of which is expected to be that of a Tomonaga-Luttinger liquid [1]. Such liquids exhibit bosonic collective low-energy excitations and spin-charge separation. Using Bragg spectroscopy and a Feshbach resonance, we directly excite either the spin or charge wave with a tunable repulsive interaction strength. We observe the onset of spin-charge separation as interactions are increased from zero. The spin and charge excitation velocities are equal for the non-interacting case, while the charge-mode velocity increases and the spin-mode velocity decreases with increasing interaction, a hallmark of spin-charge separation. The excitation spectra provide access to the dynamic structure factors of each mode, which are in quantitative agreement with the Tomonaga-Luttinger liquid theory, including nonlinear corrections due to band-curvature and back-scattering.

[1] Ruwan Senaratne, Danyel Cavazos-Cavazos, Sheng Wang, Feng He, Aashish Kafle, Ya-Ting Chang, Han Pu, Xi-Wen Guan and Randall G. Hulet, arXiv:2111.11545 [cond-mat.quant-gas]

    

Observation of confinement-induced background dimers in a 1D Fermi Gas

Ultracold atoms confined to optical lattices enable systematic studies of quantum systems in reduced dimensions. Dimensionality effects are particularly prominent in their ability to modify the two-body bound and scattering states. In free space, for example, Feshbach dimers exist only on the positive scattering length side of the Feshbach resonance, while in harmonically-confined, one-dimensional (1D) systems weakly bound molecular states have been observed on both sides of the corresponding confinement-induced resonance. Moreover, a combination of quasi-1D confinement and a negative, s-wave background scattering length is predicted to give rise to a weakly-bound molecular state with a wavefunction that extends well beyond the interparticle spacing, known as a confinement-induced background (CIB) dimer [1]. Contrary to the formation of weakly-bound Feshbach dimers, the threshold for CIB dimer formation occurs far from the Feshbach resonance. Rather, it takes place at the zero-crossing of the scattering length, where the effective 1D scattering length has a pole. Here, we report the first observation of CIB dimers in a 1D Fermi gas. We realize a pseudospin-1/2 system with the lowest- and third-to-lowest, |1〉-|3〉, hyperfine sublevels of ⁶Li. The atoms are loaded into a 2D optical lattice, thus creating an array of quasi-1D atomic waveguides.  We characterize the binding energies and the population ratio between dimers and unpaired atoms in the gas using radio-frequency spectroscopy for different confinement strengths. Although the binding energy of the CIB shallow bound state is comparable to the Fermi energy, we observe them to exhibit long (> 1s) lifetimes, perhaps because of their highly-extended anisotropic wavefunction.  We will also discuss their many-body properties in 1D.

[1] T. Kristensen and L. Pricoupenko Phys. Rev. A 91, 042703 (2015)   

Fractional excitations and spin-incoherent liquids in 1D Hubbard model

The Hubbard model has become increasingly important in condensed matter physics, quantum metrology and quantum information. In this talk, we will discuss fractional excitations and spin-incoherent liquids in the 1D repulsive Fermi-Hubbard model with di erent magnetic elds and llings. Using Bethe ansatz solution, we rigorously show that the fractional spin and charge excitations display di erent features of spin-charge separation in various lling limits. For a dilute- lled lattice, the interplay between the charge and the spin degrees of freedom can disrupt the coherent Luttinger liquids of spin and charge, giving rise to the so-called spin-incoherent liquid. Whereas near the half-lling limit, the charge velocity is exponentially suppressed, which means that the system enters the quantum critical regime, thus there exists neither spin- nor charge-incoherent liquids. Furthermore, we determine universal behaviour of such spin-coherent and -incoherent liquids in the vicinities of different phase transitions.   

Topological Exchange Statistics in One Dimension

The standard topological approach to indistinguishable particles formulates exchange statistics by using the fundamental group to analyze the connectedness of the configuration space. Although successful in two and more dimensions, this approach gives only trivial or near trivial exchange statistics in one dimension because two-body coincidences are excluded from configuration space. Instead, we include these path-ambiguous singular points and consider configuration space as an orbifold. This orbifold topological approach allows unified analysis of exchange statistics in any dimension and predicts novel possibilities for anyons in one-dimensional systems, including non-abelian anyons obeying alternate strand groups. It also clarifies the non-topological origin of fractional statistics in one-dimensional anyon models.   

Radio-frequency spectroscopy near a p-wave Feshbach resonance in one dimension

We study scattering of identical fermions confined in two orthogonal standing waves near a p-wave Feshbach resonance. By varying the lattice depth and magnetic field, we observe the confinement induced resonance shift and compare to recent parameterizations of this resonance. By performing fast radio-frequency (rf) spectroscopy, we measure the dependence of the rf spectrum on one-dimensional (1D) interaction strength. We relate the rf transfer rate through universal relations to the 1D p-wave contact, which is a measure of correlation strength in the gas. By amplitude modulating and frequency modulating the optical lattice, we test the influence of band population on the observed rf spectra.   

Thermodynamic contacts and breathing mode physics of 1D odd-wave Fermi gases in the high temperature limit

An important tool for understanding the effects of interactions in harmonically trapped atomic gases is the examination of their collective modes. One such mode is the breathing or monopole mode, which is special as it is constrained to occur at twice the harmonic trapping frequency when the interactions are scale invariant. When the interactions are not scale invariant, the frequency of the breathing mode will deviate from twice the trap frequency. The deviation itself depends on the thermodynamic contacts, which describe how the energy changes with the interactions. In this talk I study the thermodynamic contacts and the breathing mode of a spin-olarized one-dimensional Fermi gas with odd wave interactions in the high-temperature limit. In this case, the energy dependence of the interactions, characterized by the effective range, can not be neglected.  I explicitly show how the breathing mode changes with interaction strength from weak to strong interactions for a finite effective range. Such dynamics can be studied in experiments and provide a tool for understanding how the dynamics depend on interactions with a finite effective range.   

An algebraic geometric classification of the solutions of the 1D Gross-Pitaevskii equation

The stationary solutions of the Schrödinger equation with box or periodic boundaries show a clear correspondence to solutions found for the non-linear Gross-Pitaevskii equation commonly used to model Bose-Einstein condensates. However, in the non-linear case there exists an additional class of solutions for periodic boundaries first identified by L.D. Carr et al. [1]. These nodeless solutions have no corresponding counterpart in the linear case. To fully classify these solutions and to understand their origin, we study the underlying algebraic geometry. Therefore, we treat both equations in the hydrodynamic framework, resulting in a first-order differential equation for the density determined by a quadratic polynomial in the linear case and by a cubic polynomial in the non-linear case, respectively. Our approach allows for a clear geometric interpretation and complete classification of the solution space in terms of the nature and location of the roots of these polynomials. Furthermore, we consider possible generalizations of our method towards higher dimensional systems and beyond-mean-field corrections.

[1] L.D. Carr, C.W. Clark, W.P. Reinhardt, Phys. Rev. A 62, 063610 & 063611 (2000)   

Mobile dissipative impurities in one-dimensional Bose gases

We study an impurity immersed into a one-dimensional Bose gas with a fluctuating impurity-Bose interaction (i.e. a dissipative „polaron“). We use a mean-field description which takes the deformation of the quasi condensate into account such that quantum fluctuations are small. The stochastic coupling creates a coherent flow of particles towards the impurity, similar to the effect of a local loss. In addition there is an outward flowing incoherent current of particles.  Depending on the amplitude of the noise and the velocity of the impurity a normal or Zeno-like quasi stationary state emerges. Above a critical value of the velocity there is a continuous emission of solitons such that no stationary state forms even for a subsonic impurity. In the case of two impurities, we find evidence for a dissipation-mediated long-range interaction between the impurities for weak noise, while strong noise results, similar as a moving impurity, in a constant creation of solitons.    

Measuring Rapidities of a Bosonic Dipolar 1D Quantum Gas in Tonks and Super-Tonks Regimes

The distribution of rapidities—quasi-momenta of a one-dimensional (1D) many-body system that depends on the interactions within particles—are of great interest in characterizing many-body states. The bosonic 1D dipolar gas, with its integrability-breaking long-range interactions, is a perfect platform to explore rapidity distributions in a nearly integrable system. We report the measurement of rapidity distributions in a 1D dipolar quantum gas of dysprosium, where we use a Feshbach resonance to tune the short-range interaction strength and a magnetic field angle to tune the long-range dipole-dipole interaction sign and strength. In addition to ground state  measurements, we also topologically pump the gas into super-Tonks regime to measure the rapidities of prethermal long-lived excited states (akin to many-body scar states).