Ferromagnetic behavior in the strongly interacting two-component Bose gas

Abstract

We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat cv ∼ T 1/2 and the susceptibility χ ∼ T −2 are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.PACS numbers: 03.75. Hh, 03.75.Mn, 04.20.Jb, 05.30.Jp I. INTRODUCTIONExperiments with ultracold quantum gases are opening up exciting new possibilities for testing and exploring quantum effects in many-body systems (for recent reviews, see Refs. [1][2][3]). These include experiments on effectively one-dimensional (1D) quantum Bose gases of 87 Rb atoms in which the interaction strength between atoms is tunable [4][5][6][7][8]. The experiments provide a striking example of realizing an integrable quantum many-body problem. They demonstrate the explicit fermionization of bosons and provide a direct test of theoretical results obtained for the integrable 1D interacting (spinless) Bose gas [9,10]. Another frontier of activity involves spinor Bose gases of alkali atoms in which hyperfine states comprise the pseudospins [11][12][13]. In these systems quantum collisional effects can produce spatio-temporal spin oscillations (spin waves) [14][15][16][17]. The observation of collective dynamics of spin waves and spin-state segregation in trapped spinor Bose gases has stimulated a wide range of interest in studying magnetism, topological spin defects and novel quantum phase transitions in spinor Bose gases [18,19]. Two-component spinor Bose gases have been experimentally created in a magnetic trap by rotating two hyperfine states so that the two atomic hyperfine states make up a pseudo-spin doublet [20], e.g., the |F = 2, m F = −1 and |F = 1, m F = 1 hyperfine states of 87 Rb. In general, spin-independent s-wave scattering dominates interactions in alkali atomic gases. In 1D, the two-component Bose gas with spin-independent s-wave scattering can be exactly solved, like the spinless model, by means of the Bethe ansatz [21,22]. In contrast to Fermi gases, ferromagnetic order emerges in spinor Bose gases as long as the interaction is fully spin independent [15,23]. The low-energy excitations of the model split into collective excitations carrying charge and collective excitations carrying spin. The charge...

Equilibrium thermodynamic properties of interacting two-component bosons in one dimension

“…The 1CBG asymptotic behavior in τ/γ 2 is also shown in comparison with the fully polarized 2CBG ( T ). In the bottom graph we show curves with different reduced temperatures that we compare with the analytical expression at zero temperature [36]. The 2CBG is ferromagnetic here and the value of g (2) does not depend on the relative chemical potential.…”

“…Figure 3 shows that in a 2CBG at low temperature with strong , the heat capacity is similar to that of a Lieb-Liniger Bose gas contributed by phonons. If the relative chemical potential is lower or of order of the temperature, the two-component degree of freedom appears and creates peaks similarly to a paramagnetic spinor Bose gas [36]. The maximum in the specific heat moves in higher temperature as the relative chemical potential increases.…”

“…For two components and in contrast with the Fermi gas, the ground state is (pseudospin) polarized as expected from basic arguments [32] or more formally from a general theorem valid when spin-dependent forces are absent [35]. In pseudospin language, the ground state is thus ferromagnetic, and the excitations at large coupling correspond to those in an isotropic XXX ferromagnetic chain [36], revealing thermodynamic properties which are drastically different from those of the one-component Lieb-Liniger gas [37,38]. Furthermore, recent studies of the ferromagnetic ground state revealed different dispersions for the charge and pseudospin excitations, which therefore exhibit a spin-charge separation [39,40].…”

“…The thermodynamic Bethe ansatz (TBA) allows exploitation of the condition of thermal equilibrium [46,47] to obtain the Yang-Yang-Takahashi (YYT)-like equations [36,37,47] for (λ), the dressed energy, and n (k), length n string dressed energy, n = 1,2, . .…”

“…Furthermore, recent studies of the ferromagnetic ground state revealed different dispersions for the charge and pseudospin excitations, which therefore exhibit a spin-charge separation [39,40]. The regime of strong interaction is still not completely understood, and even if Girardeau's Fermi-Bose mapping has been shown and used for the study of the one-dimensional (1D) spinor Bose gases [41] leading to a paramagnetic Tonk-Girardeau regime [36], this approach fails to provide first correction terms to this fermionization regime since the discernability of the bosons is missing.…”