This paper proposes simple feedback loops, inspired from extremum-seeking, that use the photon emission times of a single quantum system following quantum Monte-Carlo trajectories in order to lock in real time a probe frequency to the system's transition frequency. Two specific settings are addressed: a 3-level system coupling one ground to two excited states (one highly unstable and one metastable) and a 3-level system coupling one excited to two ground states (both metastable). Analytical proofs and simulations show the accurate and robust convergence of probe frequency to system-transition frequency in the two cases.
This paper proposes simple feedback loops, inspired from extremum-seeking, that use the photon emission times of a single quantum system following quantum Monte-Carlo trajectories in order to lock in real time a probe frequency to the system's transition frequency. Two specific settings are addressed: a 3-level system coupling one ground to two excited states (one highly unstable and one metastable) and a 3-level system coupling one excited to two ground states (both metastable). Analytical proofs and simulations show the accurate and robust convergence of probe frequency to system-transition frequency in the two cases.
Simple feedback loops, inspired from extremum seeking, are proposed to lock a probe frequency to the transition frequency of a single quantum system following quantum Monte-Carlo trajectories. Two specific quantum systems are addressed: a 2-level one, and a 3-level one that appears in coherence population trapping and optical pumping. For both systems, the feedback algorithm is shown to be convergent in the following sense: the probe frequency converges on average towards the system-transition one and its standard deviation can be made arbitrarily small. Closed-loop simulations illustrate robustness versus jump-detection efficiency and modeling errors.
Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of feedback. In this letter we first introduce a unifying framework, based on a single general equation, that describes all possible feedback schemes in sequentially (and continuously) measured systems, and from which all previous results follow. Next, we specialize it to the case of quantum jumps and introduce a new type of feedback based on the channel of the last detected jump, as well as the time elapsed since it occurred. Our description is experimentally grounded, and naturally allows for the introduction of realistic effects, such as time-delays in the feedback loop. We illustrate our results with two time-dependent feedback protocols conditioned on quantum-jump detections: one achieving population inversion of a two-level system against a thermal bath, and another enabling real-time reversal of quantum transitions, both admitting steady-state solutions.
We examine the gain property of a probe field interacting with two different three-level Lambda-type atomic systems with an open loop or a close loop. In the atomic system with an open loop, there exists quantum interference resulting from spontaneous emissions to two near-degenerate lower levels from a common upper level, and the weak probe field can be greatly amplified due to the spontaneously generated coherence. Moreover, the probe gain becomes sensitive to the relative phase between the probe and coupling fields, so we can realize phase control of the probe gain in principle. In the atomic system with a close loop, we use a microwave field to couple the two well-spaced lower levels so that quantum coherence similar to SGC can be generated. In this atomic system, we also can achieve the phase-sensitive probe gain due to the quantum interference between two different absorption channels for the probe field. Note, only in the case of three-photon resonance, this close-loop atomic system can reach a steady state. While in the case of three-photon off-resonance, the probe gain without inversion always oscillates periodically versus time, thus no steady-state probe gain can be achieved.
A fast and robust approach to controlling the quantum state of a multi-level quantum system is investigated using a twofrequency time-varying potential. A comparison with other related approaches in the context of a two-level system is also presented, showing similar times and fidelities. As a concrete example, we study the problem of a particle in a box with a periodically oscillating infinite square-well potential, from which we obtain results that can be applied to systems with periodically oscillating boundary conditions. We show that the transition between the ground and first excited state is about 20 times faster than the one performed using a single frequency, both with fidelity of 99.97%. The transition time is about 3.5 times the minimum allowed by quantum mechanics. A test of the robustness of the approach is presented, concluding that, counter-intuitively, it is not only faster but also easier to tune up two frequencies than one. This robustness makes the approach suitable for real applications.
Fast measurement, signal processing, and accurate estimation of Hamiltonian parameters are essential for feedback control in quantum-classical interface circuitry. However, existing frequentist and Bayesian inference methods typically require a large number of measurements to achieve the accuracy needed to mitigate qubit decoherence. Consequently, feedback control of semiconductor qubits has largely been limited to single-qubit frequency stabilization, whereas two-qubit parameter stabilization remains experimentally unexplored. Here, we demonstrate a real-time feedback framework based on sequential Monte Carlo estimation using one bit of data from a single-shot measurement. Using a four-qubit semiconductor quantum dot device, we rapidly estimate individual qubit frequencies, yielding an approximately twofold increase in coherence time compared with a conventional Bayesian strategy. Moreover, sequential two-qubit parameter estimation using two bits of data enables stabilization of qubit-qubit coupling, allowing both quasi-static frequency drift and exchange-interaction noise to be estimated and suppressed. By shortening the time required for precise parameter estimation, these results demonstrate the importance of the synergistic development of classical and quantum electronics for building robust and scalable quantum technologies in fluctuating environments.
Recent realizations of single-atom trapping and tracking in cavity QED open the door for feedback schemes which actively stabilize the motion of a single atom in real time. We present feedback algorithms for cooling the radial component of motion for a single atom trapped by strong coupling to single-photon fields in an optical cavity. Performance of various algorithms is studied through simulations of single-atom trajectories, with full dynamical and measurement noise included. Closed loop feedback algorithms compare favorably to open-loop "switching" analogs, demonstrating the importance of applying actual position information in real time. The high optical information rate in current experiments enables real-time tracking that approaches the standard quantum limit for broadband position measurements, suggesting that realistic active feedback schemes may reach a regime where measurement backaction appreciably alters the motional dynamics.