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arXiv:1606.02897 · Europhysics Letters (EPL)

Competition between external and synthetic magnetic fields on a spin-1 ultracold Bose gas

Sk Noor Nabi, Saurabh Basu

Published Nov 1, 2016• 7 citations
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Abstract

We study a spin-1 ultracold Bose gas in the presence of both external and synthetic magnetic fields via mean-field approach corresponding to both signs of the spin-dependent interaction potential. The synthetic field is included through the hopping frequencies via Peierls coupling and the external field through the Zeeman interaction term to explore the influence of one over the other. The antiferromagnetic case shows that at low values of external field strengths, the spin singlet state is stable and the system is more likely in Mott insulating (MI) phase as the synthetic field is enhanced. But at large external fields, due to a competition between the hopping and the Zeeman interaction terms, the former tends to stabilize the MI phase compared to the superfluid (SF) phase, while the latter tries to destabilize the MI phase by suppressing the formation of singlet pairs. In the ferromagnetic case, insensitivity of the phase properties to the external magnetic field leads to stabilization of the MI phase with increasing synthetic magnetic field. Further the magnetization shows that there are distinct signatures of transverse polar and longitudinal ferro SF phases for both antiferromagnetic and ferromagnetic interactions, respectively.

DOI
10.1209/0295-5075/116/46001

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We study a spin-1 ultracold Bose gas in the presence of both external and synthetic magnetic fields via mean-field approach corresponding to both signs of the spin-dependent interaction potential. The synthetic field is included through the hopping frequencies via Peierls coupling and the external field through the Zeeman interaction term to explore the influence of one over the other. The antiferromagnetic case shows that at low values of external field strengths, the spin singlet state is stable and the system is more likely in Mott insulating (MI) phase as the synthetic field is enhanced. But at large external fields, due to a competition between the hopping and the Zeeman interaction terms, the former tends to stabilize the MI phase compared to the superfluid (SF) phase, while the latter tries to destabilize the MI phase by suppressing the formation of singlet pairs. In the ferromagnetic case, insensitivity of the phase properties to the external magnetic field leads to stabilization of the MI phase with increasing synthetic magnetic field. Further the magnetization shows that there are distinct signatures of transverse polar and longitudinal ferro SF phases for both antiferromagnetic and ferromagnetic interactions, respectively.
We explore the effects of a repulsive three body interaction and a synthetic gauge field on a spin-1 ultracold Bose gas on an optical lattice to study the quantum phase transition from a supeifluid (SF) to Mon insulating (MI) phase. Both effects being experimentally feasible to achieve, we also add an external Zeeman field to explore an interesting interplay among three of them. A site decoupling mean field technique, known to be an efficient marker of different quantum phases for a spinor Bose Hubbard model, is employed. Without the magnetic fields, the presence of three body interaction stabilizes all the MI lobes, excepting the first one, compared to the SF phase while in presence of the magnetic fields, the spin nematic MI phase makes inroad into the SF phase at the expense of the spin singlet MI phase.
We study the effects of a three-body interaction potential on a spin-1 ultracold Bose gas using mean-field approach (MFA). For an antiferromagnetic (AF) interaction, we have found the existence of the odd-even asymmetry in the Mott insulating (MI) lobes in the presence of both the repulsive two- and three-body interactions. In case of a purely three-body repulsive interaction, the higher-order MI lobes stabilize against the superfluid phase. Also the spin nematic (singlet) formation occurs for all the odd (even) MI lobes for the former, while there is neither any asymmetry, nor spin nematic (singlet) formation being observed for the latter case. The results are confirmed after carefully scrutinizing the spin eigenvalue and spin nematic order parameter for both the cases. We have compared our MFA results with the analytic phase diagrams obtained using a perturbation mean-field (PMFA) expansion.
We study the superfluid–Mott insulator (SF–MI) transition of a spin-1 boson system in an optical lattice, especially the responce of the system to an external magnetic field. Using the mean field theory, we obtain the phase diagram of SF–MI transition at zero temperature. For antiferromagnetic bosons, the Mott insulator region is stabilized when the number of particles per site is even. We find that only by changing the external magnetic field, the SF–MI transition is realized. On the other hand, the ferromagnetic case perfectly recovers the spin frozen case, that is already performed in experiments.
We investigate strongly correlated spin-1 ultracold gases with antiferromagnetic interactions in a three-dimensional optical lattice in the presence of an external magnetic field, based on bosonic dynamical mean-field theory. Due to the interplay of spin-dependent and quadratic Zeeman interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phases, depending on longitudinal magnetization. The dependence of first-order superfluid-insulator transition on external magnetic fields is explored. Interestingly, at low magnetic field, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the mF=−1m_F=-1mF​=−1 component demonstrates an abnormal increase with longitudinal magnetization, in contrast to weakly interacting cases.
Abstract Motivated by recent experimental processes, we systemically investigate strongly correlated spin-1 ultracold bosons trapped in a three-dimensional optical lattice in the presence of an external magnetic field. Based on a recently developed bosonic dynamical mean-field theory (BDMFT), we map out complete phase diagrams of the system for both antiferromagnetic and ferromagnetic interactions, where various phases are found as a result of the interplay of spin-dependent interaction and quadratic Zeeman energy. For antiferromagnetic interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phase, depending on longitudinal magnetization, whereas, for ferromagnetic case, a ferromagnetic-to-nematic-insulating phase transition is observed for small quadratic Zeeman energy, and the insulating phase demonstrates the nematic order for large Zeeman energy. Interestingly, at low magnetic field and finite temperature, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the m F = −1 component with antiferromagnetic interactions demonstrates an increase with longitudinal magnetization, while, for ferromagnetic case, the Zeeman component m F = 0 demonstrates a local minimum for the critical condensing temperature, in contrast to weakly interacting cases.
Abstract We study the effects of an attractive three-body interaction potential on a spin-1 ultracold Bose gas using the mean field approach (MFA). For an antiferromagnetic interaction, the third Mott insulator (MI) lobe is predominantly affected, where it completely engulfs the second and the fourth MI lobes at large values of interaction strength. However, no significant change is observed beyond the fourth MI lobe. The formation of the spin singlet (nematic) MI phase and the different order of phase transitions to the superfluid phase have been carefully scrutinized with the help of spin eigenvalues and the spin nematic order parameter. In the ferromagnetic case, the phase diagram shows similar features to that of a scalar Bose gas. We have compared our results on the MFA phase diagrams for both types of interaction potential via a perturbation expansion in both cases.