Blurring the boundary between bosons and fermions lies at the heart of a wide range of intriguing quantum phenomena in multiple disciplines, ranging from condensed matter physics and atomic, molecular, and optical physics to high-energy physics.One such example is a multicomponent Fermi gas with SUðNÞ symmetry that is expected to behave like spinless bosons in the large-N limit, where the large number of internal states weakens constraints from the Pauli exclusion principle.However, bosonization in SUðNÞ fermions has never been established in high dimensions where exact solutions are absent.Here, we report direct evidence for bosonization in a SUðNÞ fermionic ytterbium gas with tunable N in three dimensions (3D).We measure contacts, the central quantity controlling dilute quantum gases, from the momentum distribution and find that the contact per spin approaches a constant with a 1=N scaling in the low-fugacity regime consistent with our theoretical prediction.This scaling signifies the vanishing role of the fermionic statistics in thermodynamics and allows us to verify bosonization through measuring a single physical quantity.Our work delivers a highly controllable quantum simulator to exchange the bosonic and fermionic statistics through tuning the internal degrees of freedom in any generic dimensions.It also suggests a new route toward exploring multicomponent quantum systems and their underlying symmetries with contacts.
Blurring the boundary between bosons and fermions lies at the heart of a wide range of intriguing quantum phenomena in multiple disciplines, ranging from condensed matter physics and atomic, molecular, and optical physics to high-energy physics.One such example is a multicomponent Fermi gas with SUðNÞ symmetry that is expected to behave like spinless bosons in the large-N limit, where the large number of internal states weakens constraints from the Pauli exclusion principle.However, bosonization in SUðNÞ fermions has never been established in high dimensions where exact solutions are absent.Here, we report direct evidence for bosonization in a SUðNÞ fermionic ytterbium gas with tunable N in three dimensions (3D).We measure contacts, the central quantity controlling dilute quantum gases, from the momentum distribution and find that the contact per spin approaches a constant with a 1=N scaling in the low-fugacity regime consistent with our theoretical prediction.This scaling signifies the vanishing role of the fermionic statistics in thermodynamics and allows us to verify bosonization through measuring a single physical quantity.Our work delivers a highly controllable quantum simulator to exchange the bosonic and fermionic statistics through tuning the internal degrees of freedom in any generic dimensions.It also suggests a new route toward exploring multicomponent quantum systems and their underlying symmetries with contacts.
Ultracold fermions with SU(N >2) symmetry offer a unique opportunity to study quantum dynamics and interaction effects in the large spin systems that have no analogue in condensed matter physics. In this poster, we present a set of experiments on the measurement of contact parameters and collective excitations with a SU(N) Fermi gas of 173Yb atoms. First, we explore the short-range interaction effect via Tan’s contact parameters in a multi-component Fermi gas with SU(N >2) symmetry. The s-wave contact parameter is experimentally measured by recording the high-momentum tail of weakly interacting fermions. For a tunable number of spin component N with a fixed number of atoms per component, we verify the linear increase in the contact with N providing experimental confirmation of SU(N) interactions. Furthermore, we explore the momentum distribution of SU(N) fermions at the low momentum regime. Next, we measure collective excitations of a harmonically trapped twodimensional SU(N) Fermi gas. Various collective modes are investigated with a tunable number of spin component N showing a decrease in the ratio of quadruple and dipole mode with N. Our work will pave the way for the experimental study of interacting SU(N) Fermi gases with large spin.
Contact interactions play a fundamental role for understanding correlated quantum systems from microscopic models. For example, the 1/k4 momentum tail, the weight of which is known as Tan's contact, reveals a set of universal relations in interacting atomic systems. Nevertheless, the experimental measurement of contact has still remained unexplored for multi-component fermions with high spins. Here, we report on the measurement of s-wave contact parameter in a cold spin-balanced gas of 173Yb atoms with SU(N) symmetry. The high-momentum tail is recorded after time-of-flight expansion, and Tan's contact is directly quantified with a tunable number of spin component N without changing the number of atoms per component. We experimentally verify the linear increase in the contact with N providing experimental confirmation of the SU(N) interaction. Furthermore, we investigate the momentum distribution of SU(N) fermions at the low momentum regime showing that multi-component fermions with large N exhibit a more bosonic behavior. Our measurement directly reveals the interaction effect in a multi-component Fermi gas with SU(N) symmetry, and paves the way for study of many-body physics with high spins.
This thesis reports on the experimental realization of the 3D SU(N) Fermi-Hubbard model and the direct probing of the equation of state with an ultracold quantum gas of fermionic ytterbium in an optical lattice. Ultracold atoms in optical lattices constitute a flexible and highly tunable system to investigate Hamiltonians of condensed matter physics such as the Hubbard model. In particular, ytterbium atoms are ideal candidates for the realization of the Fermi-Hubbard model with SU(N)-symmetry due to a high decoupling of the nuclear spin from the electronic configuration. As a consequence of this enlarged symmetry, thermodynamic properties of the atomic sample depend on N, the number of spin components in the quantum gas, and novel, exotic phases are predicted to emerge at low temperatures. By locally probing a quantum gas of 173Yb in a 3D optical lattice, we determine the equation of state of the SU(6) and SU(3) Fermi-Hubbard model. The measurement of the equation of state allows us to obtain direct, model-independent access to the thermodynamic quantities of the lattice gas. In this way, we can characterize the crossover from a Fermi liquid to an SU(N) Mott insulator when tuning the interaction strength, and can probe the compressibility of the quantum gas in different interaction regimes. Moreover, we find a low specific entropy of the SU(6) gas below that of uncorrelated spins, indicating the presence of partial spin correlations in the atomic sample. The ability to access the equation of state of such high spin systems, as well as the low obtained entropy, represent an important step towards the realization of SU(N) spin Hamiltonians and the characterization of novel SU(N) phases.
One-dimensional spinless Bose and Fermi gases with contact interactions have the close interrelation via Girardeau's Bose-Fermi mapping, leading to the correspondences in their energy spectra and thermodynamics. However, correlation functions are in general not identical between these systems. We derive in both systems the exact universal relations for correlation functions, which hold for any energy eigenstate and any statistical ensemble of the eigenstates with or without a trapping potential. These relations include the large-momentum behaviors of static structure factors and of momentum distributions as well as energy relations, which connect the sums of kinetic and interaction energies to the momentum distributions. The relations involve two- and three-body contacts, which are the integrals of local pair and triad correlations, respectively. We clarify how the relations for bosons and fermions differ and are connected with each other. In particular, we find that the three-body contact makes no contribution to the bosonic energy relation, but it plays a crucial role in the fermionic one. In addition, we compute the exact momentum distribution for any number of fermions in the unitary limit.
In ultracold Fermi gases, the spatial dimension and the number of particles involved in interactions largely determine the behavior of the system. By exploiting harmonic trapping potentials and multiple hyperfine states, experiments wield a high degree of control over both of these parameters. In this work, we show that a nonrelativistic, one-dimensional, three-component Fermi system with three-body contact interactions exhibits a quantum anomaly, breaking the scale invariance that exists for this system classically. The exact solution of this three-body problem, wherein a bound trimer forms at arbitrarily small attractive couplings, features a correspondence to the two-dimensional, two-body Fermi system, through which we determine the first non-trivial virial coefficient. We further develop a numerical technique for solving the few-body problem for up to six particles and find that the effective interaction between two trimers is repulsive. To extend our analysis to the many-body problem, we apply the worm algorithm of quantum Monte Carlo and present results for various thermodynamic quantities. We find that for increasing attractive couplings, the system undergoes a Fermi-Fermi crossover from a set of three ideal Fermi gases to one weakly repulsive Fermi gas consisting of massive composite trimers. Finally, we adapt the three-body interaction to a two-dimensional lattice model, where we find strong evidence for a second-order phase transition with an associated reduction in a discrete global symmetry. While the exact experimental parameters we require have not yet been physically realized, our work provides a comprehensive first set of predictions for this model.
Quantum many-body physics has been studied for many decades. A lot of intriguing phenomena have been observed and theories have been developed. Yet many problems remain unsolved, which is largely due to a lack of general efficient classical computation method. One-dimensional (1D) systems have also drawn much attention over the past few decades. One reason is that many unique strongly correlated quantum phenomena only appear in low dimensions. Another reason is that many exact results can be obtained in 1D for cross benchmarking, such as Bethe Ansatz, Bosonization, Bose-Fermi mapping, etc. In addition, many numerical methods, such as Matrix-Product-State based and Monte Carlo methods, work most efficiently in 1D. In recent years, 1D quantum gases have been realized in many cold atom labs, providing experimental motivation for their studies. One of the most mysterious assumptions about a system of identical quantum particles is that the wavefunction must be symmetric (for bosons) or anti-symmetric (for fermions). This means that no two fermions can occupy the same state, while multiple occupancy is allowed for bosons. Bosons and fermions are therefore generally very different. But in 1D this distinction could become rather subtle, provided that the bosonic multiple occupancy is suppressed, which can happen if strong repulsion exists between them. However, when considering spin degrees of freedom, things become more complicated. In this work, we develop a generalized Bose-Fermi mapping theory, under which, the charge degrees of freedom is mapped to a spinless fermions, while the spin degrees of freedom to an effective spin chain. This mapping works for arbitrary spin, arbitrary trapping potentials, arbitrary spin-dependent interaction potential, and for either spinor bosons or fermions. In the strong interaction limit, the wavefunction of the system is represented by the strong coupling ansatz wavefunction (SCAW), which takes the form of a direct product of spinless fermions wavefunction and spin wavefunction. Using this mapping technique, we study the dynamics and collective modes of the system. Furthermore, we develop a very efficient method to calculate the one-body density matrix, from which we can calculate the momentum distribution of the system.