arXiv subjects

Tin-Lun Ho

Publications and source records attributed to Tin-Lun Ho.

At least 19 recordsLinked to original sources

arXiv2022

Interference of Holon Strings in 2D Hubbard Model

The 2D Hubbard model with large repulsion is a central and yet unsolved problem in condensed matter physics for decades. The challenge appears below half filling, where the system is a doped antiferromagnet. In this regime, the fermion excitations are nothing like those in a Fermi liquid, which carry both spin and charge. Rather, they split up into holons and spinons, carrying charge and spin separately. Moreover, the motion of a holon is believed to stir up the underlying antiferromagnetic order, leaving behind it a string of "wrong" spins. While direct observation of the holon string is difficult in electron systems, it has become possible in cold atom experiments due to recent experimental advances. Here, we point out the key feature of the holon strings, i.e. its Marshall phase, can be observed through measurements of spin correlations. Moreover, the interference of these strings leads to an anisotropic holon propagation clearly distinguishable than those of spinless fermions, as well as a large suppression of the magnetic order in the region swept through by the strings, as if the system is driven towards a spin liquid. We further illustrate the effect of the Marshall phase by showing the motion of a holon in the so-called $σtJ$-model where the Marshall phase is removed.

cond-mat.quant-gas↗

arXiv2021

Optimal configurations and "Pauli crystals" of quantum clusters

Broken rotational and translational symmetries are the hallmarks of solid state materials. In contrast, quantum liquids and gases do not exhibit such properties. However, if we regard the logarithm of the absolute square of a quantum liquid as an energy ${\cal E}= -{\rm ln}|Ψ|^2$, a geometric pattern naturally occurs at the minimum, i.e. the optimal configuration. Such geometric patterns have recently been studied for non-interacting fermions, and have been named "Pauli crystals". However, such patterns exist in all interacting gases (Bose or Fermi), independent of statistics. Here, we present an algorithm to determine the optimal configurations of quantum clusters solely from the images of their densities and without theoretical inputs. We establish its validity by recovering a number of exact results, showing that it can identify the changes in the cluster's ground state which corresponds to phase transitions in bulk systems.

cond-mat.quant-gas↗

arXiv2021

The Bose-Einstein Condensate of G-wave Molecules and Its Intrinsic Angular Momentum

The recent report on the realization of a Bose-Einstein condensate of G-wave molecule made up of bound pairs of Cesium bosons is a surprise. These molecules are created at the G-wave resonance at 19.87G, where the severe three-body loss usually associated with these resonance are found to be reduced significantly when the density of the gas is reduced in a quasi 2D setting. The G-wave molecules produced through this resonance have non-zero angular momentum projections, resulting in the first BEC with a macroscopic intrinsic angular momentum. Here, we show that this intrinsic angular momentum will lead to many new quantum effects. They include a splitting of collective modes in the absence of vortices, an orientation dependent energy shift due to the moment of inertia of the molecules, and a contribution to angular momentum in non-uniform magnetic fields different from that of the Berry phase current. The intrinsic angular momentum also provides a way to probe the half vortices, excitations that are unique to molecular condensates of bosons. The wavefunction giving rise to the intrinsic angular momentum can also be mapped out from the noise correlation.

cond-mat.quant-gas↗

arXiv2020

Imaging the Holon String by Quantum Interference

It has been a long sought goal of Quantum Simulation to find answers to long standing questions in condensed matter physics. A famous example is the ground and the excitations of 2D Hubbard model with strong repulsion below half filling. The system is a doped antiferromagnet. It is of great interests because of its possible relation to high Tc superconductor. Theoretically, the fermion excitations of this model are believed to split up into holons and spinions, and a moving holon is believed to leave behind it a string of "wrong" spins that mismatch with the antiferromagnet background. Here, we show that the properties of the ground state wavefunction and the holon excitation of the 2D Hubbard model can be revealed in unprecedented detail using the technique of quantum interference in atomic physics. This is achieved by using quantum interference to measure the Marshall sign of the doped antiferromanget. The region of wrong Marshall sign directly reflects the spatial extent of fluctuating string attached to the holon.

cond-mat.quant-gas↗

arXiv2019

Universal Features of Landau Fans of Twisted Bilayer Graphene with Large Superlattices

Current experiments on different samples of twisted bilayer graphene (TBG) have found different sets of insulating phases. Despite this diversity, many features of these insulating phases appear to be universal. They include the dispersion of Landau fans away from charge neutrality, a reduced Landau fan degeneracy from the expected value at charge neutrality, and the further reduction of this degeneracy when crossing an insulating phase with odd number of electrons in the superlattice unit cell. We point out that all these behaviors as well as the ferromagnetic behavior observed in some of the insulating states suggest an underlying "ideal" pattern, with different part of it realized in the different samples in different experiments. We further show that such pattern can be accounted for by a Hubbard like model for the superlattice augmented with a set of chemical potential dependent mean fields that break the symmetry of the eight internal degrees of freedoms successively. The simultaneous importance of Mott like physics and mean field physics may be a general feature of twisted 2D electronic materials with large superlattices, not necessarily confined to graphene.

cond-mat.str-el↗

arXiv2018

Majorana edge state in a number-conserving Fermi gas with tunable p-wave interaction

The remarkable properties and potential applications of Majorana fermions have led to considerable efforts in recent years to realize topological matters that host these excitations. For a number-conserving system, there have been a few proposals, using either coupled-chain models or multi-component system with spin-orbit coupling, to create number fluctuation of fermion pairs in achieving Majorana fermion. In this work, we show that Majorana edge states can occur in a spinless Fermi gas in 1D lattices with tunable $p$-wave interaction. This is facilitated by the conversion between a pair of (open-channel) fermions and a (close-channel) boson, thereby allowing the number fluctuation of fermion pairs in a single chain. This scheme requires neither spin-orbit coupling nor multi-chain setup and can be implemented easily. Using the density-matrix-renormalization-group method, we have identified the Majorana phase in a wide range of parameter regime as well as its associated phase transitions. The topological nature of the Majorana phase manifests itself in a strong edge-edge correlation in an open chain that is robust against disorder, as well as in a non-trivial winding number in the bulk generated by using twisted boundary condition. It is also shown that the Majorana phase in this system can be stable against atom losses due to few-body collisions on the same site, and can be easily identified from the fermion momentum distribution. These results pave the way for probing the intriguing Majorana physics in a simple and stable cold atoms system.

cond-mat.quant-gas↗

arXiv2018

Potential Scattering on a Spherical Surface

The advances in cold atom experiments have allowed construction of confining traps in the form of curved surfaces. This opens up the possibility of studying quantum gases in curved manifolds. On closed surfaces, many fundamental processes are affected by the local and global properties, i.e. the curvature and the topology of the surface. In this paper, we study the problem of potential scattering on a spherical surface and discuss its difference with that on a 2D plane. For bound states with angular momentum $m$, their energies ($E_{m}$) on a sphere are related to those on a 2D plane ($-|E_{m,o}|$) as $E_{m}= - |E_{m, o}| + E_{R}^{} \left[ \frac{m^2-1}{3} + O\left( \frac{r_o^2}{R^2} \right) \right] $, where $E_{R}^{} = \hbar^2/(2M R^2)$, and $R$ is the radius of the sphere. Due to the finite extent of the manifold, the phase shifts on a sphere at energies $E\sim E_{R}^{}$ differ significantly from those on a 2D plane. As energy $E$ approaches zero, the phase shift in the planar case approaches $0$, whereas in the spherical case it reaches a constant that connects the microscopic length scale to the largest length scale $R$.

cond-mat.quant-gas↗

arXiv2017

The Chern Numbers of Interaction-stretched Monopoles in Spinor Bose Condensates

Using the Dirac and the Yang monopole in spinor condensates as examples, we show that interactions can stretch the point singularity of a monopole into an extended manifold, whose shape is strongly influenced by the sign of interaction. The singular manifold will cause the first and second Chern number to assume non-integer values when it intersects the surface on which the Chern numbers are calculated. This leads to a gradual decrease of the Chern numbers as the monopole moves away from the surface of integration, instead of the sudden jump characteristic of a point monopole. A gradual change in $C_2$ has in fact been observed in the recent experiment by Spielman's group at NIST. By measuring the range of non-integer values of the Chern numbers as the monopole moves away from the surface of integration along different directions, one can map out the shape of the singular manifold in the parameter space.

cond-mat.quant-gas↗

arXiv2017

Symmetry-enforced quantum spin Hall insulators in $π$-flux models

We prove a Lieb-Schultz-Mattis theorem for the quantum spin Hall effect (QSHE) in two-dimensional $π$-flux models. In the presence of time reversal, $U(1)$ charge conservation and magnetic translation (with $π$-flux per unit cell) symmetries, if a generic interacting Hamiltonian has a unique gapped symmetric ground state at half filling (i.e. an odd number of electrons per unit cell), it can only be a QSH insulator. In other words, a trivial Mott insulator is forbidden by symmetries at half filling. We further show that such a symmetry-enforced QSHE can be realized in cold atoms, by shaking an optical lattice and applying a time-dependent Zeeman field.

cond-mat.str-el↗

arXiv2016

Energy Cascade in Quantum Gases

Energy cascade is ubiquitous in systems far from equilibrium. Facilitated by particle interactions and external forces, it can lead to highly complex phenomena like fully developed turbulence, characterized by power law velocity correlation functions. Yet despite decades of research, how these power laws emerge from first principle remains unclear. Recently, experiments show that when a Bose condensate is subjected to periodic shaking, its momentum distribution exhibits a power law behavior. The flexibility of cold atom experiments has provided new opportunities to explore the emergence of these power laws, and to disentangle different sources of energy cascade. Here, we point out that recent experiments in cold atoms imply that classical turbulence is part of a larger family of scale invariant phenomena that include ideal gases. Moreover, the property of the entire family is contained in the structure of its Floquet states. For ideal gases, we show analytically that its momentum distribution acquires a $1/q^2$ tail in each dimension when it is shaken periodically.

cond-mat.quant-gas↗

arXiv2016

Fusing Quantum Hall States in Cold Atoms

Realizing quantum Hall states in a fast rotating Bose gas is a long sought goal in cold atom research. The effort is very challenging because Bose statistics fights against quantum Hall correlations. In contrast, Fermi statistics does not cause such conflict. Here, we show that by sweeping the integer quantum Hall states of a spin-1/2 Fermi gas across the Feshbach resonance from the BCS side to the BEC side at a "projection" rate similar to that in the "projection" experiment of fermion superfluid, these states can be "fused" into a bosonic quantum Hall states. A projection sweep means the pair association is sufficiently fast so that the center of mass of the pair remains unchanged in the process. We show that the fusion of integer fermion states with filling factor $ν_{\uparrow}=ν_{\downarrow}=n$ will result in a bosonic Laughlin state and Pfaffian state for $n=1$ and 2. The is due to a hidden property of the fermionic integer quantum Hall states -- for any grouping of opposite spin into pairs, their centers of mass automatically assume a bosonic quantum Hall structure.

cond-mat.quant-gas↗

arXiv2015

Spin and charge modulations in a single hole doped Hubbard ladder -- verification with optical lattice experiments

We show that pronounced modulations in spin and charge densities can be induced by the insertion of a single hole in an otherwise half-filled 2-leg Hubbard ladder. Accompanied with these modulations is a loosely bound structure of the doped charge with a spin-1/2, in contrast to the tightly bound case where such modulations are absent. These behaviors are caused by the interference of the Berry phases associated a string of flipped spins (or "phase strings") left behind as a hole travels through a spin bath with a short-range anti-ferromagnetic order. The key role of the phase strings is also reflected in how the system respond to increasing spin polarization, increasing the on-site repulsion, addition of a second hole, and increasing asymmetry between intra- and inter-chain hopping. Remarkably, all these properties persist down to ladders as short as $\sim 10$ sites. They can therefore be studied in cold atom experiments using the recently developed fermion microscope.

cond-mat.quant-gas↗

arXiv2015

The Local Spin Structure of Large Spin Fermions

We show that large spin fermions have very rich spin structures. The local spin order of a spin-$f$ Fermi gas is a linear combination of $2f$ (particle-hole) angular momentum states, $L=1,..,2f$. $L=1, 2$ represent ferromagnetic and nematic spin order, while $L\geq 3$ are higher spin orders that has no analog in spin-1/2 systems. Each $L$ spin sector is characterized as $L$ pairs of antipodal points on a sphere. Model calculations show that some of these spin-orders have the symmetry of Platonic solid, and many of them have non-abelian line defects.

cond-mat.quant-gas↗

arXiv2015

Spinor Condensates on a Cylindrical Surface in Synthetic Gauge Fields

We point out that by modifying the setup of a recent experiment that generates a Dirac string, one can create a quasi 2D spinor Bose condensate on a cylindrical surface with a synthetic magnetic field pointing radially outward from the cylindrical surface. The synthetic magnetic field takes the form of the Landau gauge. It is generated by the Berry's phase of a spin texture, frozen by an external quadrupolar magnetic field. Unlike in the planar case, there are two types of vortices (called A and B) with the same vorticity. The ground state for $5\le S\le 9$ consists of a row of alternating AB vortices lying at the equatorial circle of the cylinder. For higher values of $S$, the A and B vortices split into two rows and are displaced from each other along the cylindrical axis $z$. The fact that many properties of a BEC are altered in a cylindrical surface implies many rich phenomena will emerge for ground states in curved surfaces.

cond-mat.quant-gas↗

arXiv2014

Spin-Orbit Coupled One-Dimensional Fermi Gases with Infinite Repulsion

The current efforts of studying many-body effects with spin-orbit coupling (SOC) using alkali-metal atoms are impeded by the heating effects due to spontaneous emission. Here, we show that even for SOCs too weak to cause any heating, dramatic many-body effects can emerge in a one-dimensional(1D) spin 1/2 Fermi gas provided the interaction is sufficiently repulsive. For weak repulsion, the effect of a weak SOC (with strength $Ω$) is perturbative. inducing a weak spin spiral (with magnitude proportional to $Ω$). However, as the repulsion $g$ increases beyond a critical value ($g_c\sim 1/Ω$), the magnitude of the spin spiral rises rapidly to a value of order 1 (independent of $Ω$). Moreover, near $g=+\infty$, the spins of neighboring fermions can interfere destructively due to quantum fluctuations of particle motion, strongly distorting the spin spiral and pulling the spins substantially away from the direction of the local field at various locations. These effects are consequences of the spin-charge separation in the strongly repulsive limit. They will also occur in other 1D quantum gases with higher spins.

cond-mat.quant-gas↗

arXiv2014

Ground-State Ferromagnetic Transition in Strongly Repulsive One-Dimensional Fermi Gases

We prove that as a one-dimensional Fermi gas is brought across the resonance adiabatically from large repulsion to large attraction, the singlet ground state will give way to the maximum spin state, which is the lowest energy state among the states accessible to the system in this process. In the presence of tiny symmetry breaking fields that destroy spin conservation, the singlet ground state can evolve to the ferromagnetic state or a spin segregated state. We have demonstrated these effects by exact calculations on fermion cluster relevant to current experiments, and have worked out the quantum mechanical wavefunction that exhibits phase separation.

cond-mat.quant-gas↗

arXiv2013

Synthetic Gauge Field with Highly Magnetic Lanthanide Atoms

We present a scheme for generating a synthetic magnetic field and spin-orbit coupling via Raman coupling in highly magnetic lanthanide atoms such as dysprosium. Employing these atoms offer several advantages for realizing strongly correlated states and exotic spinor phases. The large spin and narrow optical transitions of these atoms allow the generation of synthetic magnetic fields an order of magnitude larger than those in the alkalis, but with considerable reduction of the heating rate for equal Raman coupling. The effective hamiltonian of these systems differs from that of the alkalis' by an additional nematic coupling term, which leads to a phase transition in the dressed states as detuning varies. For \text{high-spin} condensates, spin-orbit coupling leads to a spatially periodic structure, which is described in Majorana representation by a set of points moving periodically on a unit sphere. We name this a "Majorana spinor helix" in analogy to the persistent spin-1/2 helix observed in electronic systems.

cond-mat.quant-gas↗

arXiv2013

Phase Separation in Mixtures of Repulsive Fermi Gases Driven by Mass Difference

We show that phase separation must occur in a mixture of fermions with repulsive interaction if their mass difference is sufficiently large. This phenomenon is highly dimension-dependent. Consequently, the density profiles of phase separated 3d mixtures are very different from those in 1d. Noting that the ferromagnetic transition of a spin-1/2 repulsive Fermi gas is the equal mass limit of the phase separation in mixtures, we show from the Bethe Ansatz solution that a ferromagnetic transition will take place in the scattering states when the repulsive interaction passes through resonance and becomes attractive.

cond-mat.quant-gas↗