Cavityless self-organization of ultracold atoms due to the feedback-induced phase transition

Abstract

feedback is a general idea of modifying system behavior depending on the measurement outcomes. It spreads from natural sciences, engineering, and artificial intelligence to contemporary classical and rock music. Recently, feedback has been suggested as a tool to induce phase transitions beyond the dissipative ones and tune their universality class. Here, we propose and theoretically investigate a system possessing such a feedback-induced phase transition. the system contains a Bose-einstein condensate placed in an optical potential with the depth that is feedback-controlled according to the intensity of the Bragg-reflected probe light. We show that there is a critical value of the feedback gain where the uniform gas distribution loses its stability and the ordered periodic density distribution emerges. Due to the external feedback, the presence of a cavity is not necessary for this type of atomic self-organization. We analyze the dynamics after a sudden change of the feedback control parameter. The feedback time constant is shown to determine the relaxation above the critical point. We show as well that the control algorithm with the derivative of the measured signal dramatically decreases the transient time. Feedback control is known to be a useful tool to modify dynamics of classical 1 as well as quantum systems 2. There were many theoretical proposals 3-13 and several experimental realizations 14-18 of quantum feedback control in optics and atomic physics. The feedback control of quantum systems is fundamentally different from that of classical systems mainly due to the inevitable measurement back-action 19. In most cases this quantum effect does not pose sever limitations on the feasibility of feedback control, but it has to be taken into account designing quantum control algorithms 20. Recently the feedback loop has been suggested as a tool to control phase transitions in quantum systems 21 and, in particular, in many-body settings 13,22. The feedback control of atomic self-organization has been recently demonstrated experimentally in 23. Thus the new class of feedback phase transitions (FPT) has been introduced, which can have properties beyond dissipative phase transitions in open systems. The key advantage of FPT is its extremely high degree of flexibility and controllability, which allows for the manipulation of the critical point and critical exponents and, therefore, enables the tuning and control of the universality class of phase transitions 21. In this report we apply the concept of FPT to a system based on Bragg light scattering from a Bose-Einstein condensate (BEC). Instead of the self-formed standing-wave potential 24,25 , we propose to use an actively controlled optical lattice with the control based on the Bragg-reflected signal of a probe light. The system with active feedback provides much higher degree of control on the distribution of atoms and its evolution around the critical point in comparison to systems without feedback. Such improved controllability can assist in quantum simulations, ...

Spin Entanglement and Magnetic Competition via Long-Range Interactions in Spinor Quantum Optical Lattices

“…These useful features can be further explored relative to quantum information and topological order [46]. In combination with measurement it is feasible to have dynamical order control in passive measurement setups [27,28], the inclusion of feedback protocols to tailor criticality, their dynamics and study the interplay with time crystals [47][48][49][50][51].…”

Tuning the universality class of phase transitions by feedback: Open quantum systems beyond dissipation

“…Thus it would be even beneficial to have a cavity that produces only little effect on the atoms. Moreover, having enough sensitivity of light detectors the feedback scheme can possibly be realized without a cavity [2]. The Hamiltonian of the atoms and the cavity modes reads…”

“…In Eq. ( 6) we introduced the notations: δ = ω 1 − ω 0 + N g 2 1 /(2∆ a ) is the detuning of the pump mode and the measured mode including the dispersive shift, ω R = k 2 1 /2m a is the recoil frequency, the effective coupling rate is g = Ω p g 0 (N/2)/∆ a with the pump Rabi frequency Ω p = g pump a pump . The feedback is performed via GI(t) = N/8V (t).…”

“…In our letter [1], we have studied feedback-induced phase transitions (FPT) [1][2][3] in open quantum systems, which are not dissipative ones, but are coupled to a measurement device. The first experiment implementing the feedback control of Dicke phase transition using a Bose-Einstein condensate (BEC) trapped in a cavity has been reported in Ref.…”

“…We have shown that adding the measurement-based feedback can induce phase transitions. Moreover, the feedback allows for controlling quantum properties of the transition by tuning its critical exponents, and thus their universality class [1,2]. In the perspective of such feedback-induced phase transitions the role of quantum fluctuations becomes especially emphasized.…”