Fast control of topological vortex formation in Bose-Einstein condensates by counterdiabatic driving

Abstract

Topological vortex formation has been known as the simplest method for vortex formation in BEC of alkali atoms. This scheme requires inversion of the bias magnetic field along the axis of the condensate, which leads to atom loss when the bias field crosses zero. In this Letter, we propose a scheme with which the atom loss is greatly suppressed by adding counter-diabatic magnetic field. A naive counter-diabatic field violates the Maxwell equations and we need to introduce an approximation to make it physically feasible. The resulting field requires an extra currents, which is experimentally challenging. Finally we solve this problem by applying a gauge transformation so that the counter-diabatic field is generated by controlling the original trap field with the additional control of the bias field.PACS numbers: 02.30. Yy, 37.90.+, 67.85.Fg, 03.75.Lm Demonstration of quantized vortices in a superfluid is a manifestation of the nonvanishing order parameter. Topological structure of vortices often reflects the manifold of the order parameter space. It is, therefore, natural to seek for the method to experimentally demonstrate formation of vortices once BEC of alkali metal atoms has been realized. Topological method of vortex formation is the simplest one compared with other proposals, where the spinor structure of the order parameter is fully utilized [1][2][3][4][5][6][7]. Although the vortex [6] and monopole [8,9] in BEC have been observed experimentally, establishment of methods to create such interesting quantum states more accurately in time much shorter than coherence time is important for further experimental study and applications.A condensate in the weak field seeking state (WFSS) is trapped in a quadrupole magnetic field in the xy-plane with a uniform bias field along the z-axis first and, subsequently, the bias field is reversed from B z to −B z adiabatically. Then a vortex with the winding number 2F is formed, were F is the quantum number of the hyperfine spin of the condensate. This theoretical proposal has been demonstrated experimentally by several groups [10][11][12][13][14][15]. A part of the condensate is lost while vortex formation takes place. This is due to the fact that the gap between the WFSS and the neutral state (NS) and the strong field seeking state (SFSS) is gradually closed near the center of the condensate during the vortex formation and the atoms in the trapping WFSS make transition to the NS and the SFSS through the Majorana flops. It is the purpose of this Letter to show that it is possible to suppress the Majorana flops so that more atoms are left in the trap when a vortex is formed. It is certainly desirable to have more atoms left in the trap since higher atomic density implies (i) easier measurement of physical quantities (ii) fighting against atom loss due to hyperfine spin changing collision and (iii) smaller vortex core size, which is advantageous for forming a vortex in an arbitrary position in the condensate [16]. Motivated by the concept of shortcuts to adiabaticity [17...

Counterdiabatic vortex pump in spinor Bose-Einstein condensates

“…In order to make this scheme experimentally convenient, we consider a time-dependent unitary transformation U (t) = exp [−iα(t)F z ], similar to that in Ref. [47], which introduces a position-independent rotation of an angle…”

“…In contrast to the earlier work in Ref. [45], here we consider an optically trapped condensate and the magnetic field is primarly used only to control the spin state. Hence, we are free to choose also the magnetically untrapped SFSS as the initial state.…”

“…Therefore, it can be utilized to overcome several problems in adiabatic quantum control, for example, in cases in which the population transfer efficiency is limited by decoherence, three-body losses, and external noise in the control parameters of, e.g., isolated atoms and molecules [36,40,41], spin chain systems [42,43], Bose-Einstein condensates [44,45], and electron spin of a single nitrogen-vacancy center in a diamond [46]. Very recently, the CD protocol was also found to speed up the topological phase imprinting method [47]. However, vortex pumping using the CD protocol has not been reported to date.…”

Quantum knots in Bose-Einstein condensates created by counterdiabatic control

“…Here, in contrast, we show that the knot configuration can be created using a dynamic magnetic field control obtained from the CD scheme [39,40]. In the CD scheme, we first select the reference adiabatic dynamics of the spin degree of freedom corresponding to the instantaneous eigenstates of the Zeeman Hamiltonian…”

Fast-forward scaling theory for phase imprinting on a BEC: creation of a wave packet with uniform momentum density and loading to Bloch states without disturbance

“…In this paper, we study phase imprinting on the order parameter of BECs with the fast-forward scaling theory showing the nontrivial scaling property. In contrast to the various phase imprinting protocols previously proposed or demonstrated, e.g., [45][46][47][48][49][50][51][52][53][54][55][56], our phase imprinting protocol is based on the nontrivial scaling property of quantum dynamics. The theory is applied to derive the driving potential for creation of a peculiar state, a wave packet with uniform momentum density (WPUM), which is introduced in this paper.…”