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arXiv:1609.02180 · Physical Review Letters

Phase Transitions in Definite Total Spin States of Two-Component Fermi Gases

Vladimir Yurovsky

Published May 19, 2017• 4 citations
arXivHTMLPDF

Abstract

Second-order phase transitions have no latent heat and are characterized by a change in symmetry. In addition to the conventional symmetric and antisymmetric states under permutations of bosons and fermions, mathematical group-representation theory allows for non-Abelian permutation symmetry. Such symmetry can be hidden in states with defined total spins of spinor gases, which can be formed in optical cavities. The present work shows that the symmetry reveals itself in spin-independent or coordinate-independent properties of these gases, namely as non-Abelian entropy in thermodynamic properties. In weakly interacting Fermi gases, two phases appear associated with fermionic and non-Abelian symmetry under permutations of particle states, respectively. The second-order transitions between the phases are characterized by discontinuities in specific heat. Unlike other phase transitions, the present ones are not caused by interactions and can appear even in ideal gases. Similar effects in Bose gases and strong interactions are discussed.

DOI
10.1103/physrevlett.118.200403

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Second-order phase transitions have no latent heat and are characterized by a change in symmetry. In addition to the conventional symmetric and antisymmetric states under permutations of bosons and fermions, mathematical group-representation theory allows for non-Abelian permutation symmetry. Such symmetry can be hidden in states with defined total spins of spinor gases, which can be formed in optical cavities. The present work shows that the symmetry reveals itself in spin-independent or coordinate-independent properties of these gases, namely as non-Abelian entropy in thermodynamic properties. In weakly interacting Fermi gases, two phases appear associated with fermionic and non-Abelian symmetry under permutations of particle states, respectively. The second-order transitions between the phases are characterized by discontinuities in specific heat. Unlike other phase transitions, the present ones are not caused by interactions and can appear even in ideal gases. Similar effects in Bose gases and strong interactions are discussed.
Many-body systems of identical arbitrary-spin particles, with separable spin and spatial degrees of freedom, are considered. Their eigenstates can be classified by Young diagrams, corresponding to nontrivial permutation symmetries (beyond the conventional paradigm of symmetric-antisymmetric states). The present work obtains the following. (a) Selection rules for additional nonseparable (dependent on spins and coordinates) k-body interactions: the Young diagrams, associated with the initial and final states of a transition, can differ by relocation of no more than k boxes between their rows. (b) Correlation rules in which eigenstate-averaged local correlations of k particles vanish if k exceeds the number of columns (for bosons) or rows (for fermions) in the associated Young diagram. It also elucidates the physical meaning of the quantities conserved due to permutation symmetry-in 1929, Dirac identified those with characters of the symmetric group-relating them to experimentally observable correlations of several particles. The results provide a way to control the formation of entangled states belonging to multidimensional non-Abelian representations of the symmetric group. These states can find applications in quantum computation and metrology.
The thermodynamic properties of two-component Fermi gases with divergent scattering length is investigated and the transition temperature for the emergence of a stable dimeric gas is obtained by a simple theoretical model where the unique property of the dimers (i.e. fermionic atom pairs) with divergent scattering length is considered. Below the transition temperature, through the investigation of the overall entropy for the mixture gas of fermionic atoms and dimers, we calculate the relation between the energy and temperature of the system. In the limit of zero temperature, based on the chemical equilibrium condition, the fraction of the dimers is investigated and the role of the dimers in the collective excitations of the system is also discussed. It is found that our theoretical results agree with the condensate fraction, collective excitations, transition temperature and heat capacity investigated by the recent experiments about the strongly interacting two-component Fermi gases.
In a spinor Bose-Einstein gas, the non-zero hyperfine spin of the gas becomes an accessible degree of freedom. At low temperature, such a gas shows both magnetic and superfluid order, and undergoes both density and spin dynamics. These lecture notes present a general overview of the properties of spinor Bose-Einstein gases. The notes are divided in five sections. In the first, we summarize basic properties of multi-component quantum fluids, focusing on the specific case of spinor Bose-Einstein gases and the role of rotational symmetry in defining their properties. Second, we consider the magnetic state of a spinor Bose-Einstein gas, highlighting effects of thermodynamics and Bose-Einstein statistics and also of spin-dependent interactions between atoms. In the third section, we discuss methods for measuring the properties of magnetically ordered quantum gases and present newly developed schemes for spin-dependent imaging. We then discuss the dynamics of spin mixing in which the spin composition of the gas evolves through the spin-dependent interactions within the gas. We discuss spin mixing first from a microscopic perspective, and then advance to discussing collective and beyond-mean-field dynamics. The fifth section reviews recent studies of the magnetic excitations of quantum-degenerate spinor Bose gases. We conclude with some perspectives on future directions for research.
In this thesis, we investigate thermodynamic properties, magnetic phase transitions and correlation functions of integrable quantum many-body systems in the field of ultracold atomic gases. The scope of our investigation encompasses three models in one-dimension that are integrable by means of the Bethe ansatz method. They are the multi-component 5-interacting Fermi gas, the spin-l Bose gas with antiferromagnetic spin interaction and the SU(2) spinor Bose gas with finite-range Gaussian interaction. We derive the thermodynamic Bethe ansatz equations for the general SU(k) Fermi gas. We illustrate the root patterns and give a quantitative description of the ground state properties for the strongly and weakly interacting regimes. The thermodynamics and magnetic phase transitions are described quantitatively by means of the thermodynamic Bethe ansatz equations. We find that all phase transitions in the attractive regime are of second order with a linear field dependent magnetization in the vicinities of critical points. The SU(2) Fermi gas is studied in more detail. The low temperature thermodynamics for the repulsive case is derived by means of the Wiener-Hopf technique. Finite-size corrections and correlation functions for both the repulsive and attractive cases are derived from the nested Bethe ansatz equations and conformal field theory. In the attractive case, we show that spatial oscillations of the leading terms in the pair correlation function and spin correlation function solely depend on the mismatch between Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristic of a Fulde- Ferrell-Larkin-Ovchinnikov (FFLO) state. For the spin-l Bose gas with antiferromagnetic spin interaction, we find that at zero temperature, the system exhibits three quantum phases: a phase with singlet pairs of bosons, a fully-polarized Tonks-Girardeau gas phase of unpaired ms = 1 bosons, and a mixed phase of singlet pairs and unpaired ms = 1 bosons. Phase transitions in the vicinities of the critical fields are also of second order with a linear field dependent magnetization. Finally, we use the asymptotic Bethe ansatz method to derive the quasimomenta distribution and ground state energy for the SU(2) spinor Bose gas with finite-range Gaussian interaction. We show that finite range potentials are more likely to lead to quasi Bose-Einstein condensation than zero range potentials by studying the spatial density profiles as the interaction width increases.
We investigate strongly correlated phases of two-component (or pseudospin-1/21/21/2) Bose gases under rapid rotation through exact diagonalization on a torus geometry. In the case of pseudospin-independent contact interactions, we find the formation of gapped spin-singlet states at the filling factors $\ensuremath{\nu}=k/3+k/3$ (k/3k/3k/3 filling for each component) with integer kkk. We present numerical evidences that the gapped state with k=2k=2k=2 is well described as a non-Abelian spin-singlet (NASS) state, in which excitations feature non-Abelian statistics. Furthermore, we find the phase transition from the product of composite fermion states to the NASS state by changing the ratio of the intercomponent-to-intracomponent interactions.