Spontaneous $\mathcal{PT}$ symmetry breaking of a ferromagnetic superfluid in a gradient field

Abstract

We consider the interaction of a ferromagnetic spinor Bose-Einstein condensate with a magnetic field gradient. The magnetic field gradient realizes a spin-position coupling that explicitly breaks time-reversal symmetry T and space parity P, but preserves the combined PT symmetry. We observe using numerical simulations, a phase transition spontaneously breaking this remaining symmetry. The transition to a low-gradient phase, in which gradient effects are frozen out by the ferromagnetic interaction, suggests the possibility of high-coherence magnetic sensors unaffected by gradient dephasing.PACS numbers: 67.85. Fg, 64.60.Ej Introduction -The discovery of the very complex vacuum in superfluid 3 He proved to be highly stimulating to the theory of symmetry breaking [1] and topological defects [2,3]. New features of quantum gases emerged with the first realizations of spinor Bose-Einstein condensates (SBEC) [4,5], thanks to the many degrees of freedomboth internal and external -and to the excellent control of the experimental parameters. SBECs are extremely rich and versatile systems to study complex quantum vacuua [6], for example to test the validity of universal phenomena like the Kibble-Zurek mechanism [7-9], or to study Goldstone modes such as gapless magnons [10].The coupling of SBECs to magnetic fields has been exploited to study quantum phase transitions in SBECs [11][12][13], and to realize point-like topological defects such as Dirac monopoles [14-16] and 2D skyrmions [17]. In these works, spin symmetries and topology were induced by strong gradients, e.g. 37 mT/m in Ref. [14]. Here we show that via a quantum phase transition at lower gradients ∼ 0.5 mT/m, the ferromagnetic interaction can "freeze out" the gradient effect. This suggests the possibility of magnetic sensors free from gradient dephasing, a practical limitation in coherent magnetometry [18][19][20][21][22][23][24].We use group theoretical methods that have proven fruitful in the analysis and classification of SBEC phases [1,25]. The interaction with the gradient realizes an interesting spin-position coupling that explicitly breaks the parity P and time-reversal T symmetries, only preserving the combined PT symmetry. Numerically solving the Gross-Pitaevskii equations of the system, we observe that below a critical value of the magnetic field gradient, the PT symmetry is spontaneously broken and a nonzero overall magnetization appears. This occurs when the ferromagnetic interactions dominate the coupling energy between the gradient field and the spins, resulting in a globally polarized condensate. Moreover, we observe that this effect is associated with a phase transition. Interestingly, discrete, and in particular PT , symmetry breaking is also observed in Bose gases with spin-orbit coupling [26][27][28].

Non-Hermitian noncommutative quantum mechanics

“…There is a strong research activity in the field of non-Hermitian quantum mechanics, both as regards its foundation [7,8] and its application to a wide variety of phenomena, such as for metrology [9], chaos in optomechanics [10,11], and for stimulating the fluctuation superconductivity [12]. The finding of PT -symmetry breaking leading to the coalescence of the energy levels has also been reported in distinct systems as microwave billiard [13], tunneling heterostructures [14], lattice model [15], a ferromagnetic superfluid [16], etc., considerably broadening the range of interest in the physics of non-Hermitian Hamiltonians.…”

Bose-Einstein Condensate Comagnetometer

“…SBECs can have high densities and multi-second magnetic coherence times [26], which together imply extreme magnetic sensitivity at the few-µm length scale [27]. A single mode SBEC comagnetometer is robust against external magnetic field gradients [28] and could find application in detecting shortrange spin-dependent forces [29] and in studying cold collision physics [30]. We employ a 87 Rb SBEC, with the f = 1 and f = 2 hyperfine manifolds as co-located magnetic sensors.…”