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.
Highlights
Feedback is a general idea of modifying system behavior depending on the measurement outcomes
The key advantage of feedback phase transitions (FPT) is its extremely high degree of flexibility and controllability, which allows for the manipulation of the critical point and critical exponents and, enables the tuning and control of the universality class of phase transitions[21]
We presented the FPT in the system with atomic Bose-Einstein condensate (BEC), where the probe light was Bragg-scattered from BEC and used to control the additional optical lattice potential for the atoms
Summary
Feedback is a general idea of modifying system behavior depending on the measurement outcomes. The feedback control of quantum systems is fundamentally different from that of classical systems mainly due to the inevitable measurement back-action[19]. 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 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, based on ultracold quantum gases[26,27,28,29,30]. It will be intriguing to study, how more advanced methods than the feedback control can influence quantum systems, for example, applying the digital methods of machine learning and artificial intelligence in real time
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