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International Journal of Advanced Natural Sciences and Engineering Researches

Feedback Control over Quantum Sensing Based on Bose-Einstein Condensate Trapped in Two-Dimensional Ring Potential

Sergey Borisenok

Published Oct 13, 2024• 0 citations
OpenAlex

Abstract

Recent great progress in studying theoretical and especially experimental properties of Bose Einstein condensate (BEC) creates a new era in developing and designing principally novel types of quantum devices, including quantum sensors for measuring nonlinear interactions, external electrical and magnetic fields, and other physical characteristics with high sensitivity. Here we discuss the application of feedback control over a quantum sensor based on the Bose-Einstein condensate trapped in two dimensional ring potential. For a weakly interacting regime, the dynamics of such a system are modeled by three coupled complex differential master equations containing the parameter of interaction and the chemical potential parameter. The last one plays the role of control variable in sensing protocol for two body interaction. The goal of control is to minimize the effects of the higher energy levels in BEC by driving their corresponding matrix density elements. The control algorithm is designed as Kolesnikov’s feedback forming an artificial target attractor in the dynamical system. We re-formulate Kolesnikov’s approach in the operator form to adapt it to quantum engineering processes. The control approach proposed here can be efficiently extended to different sensing protocols for detecting external magnetic fields, rotational components, and other physical characteristics of BEC interacting with the environment.

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Recent great progress in studying theoretical and especially experimental properties of Bose Einstein condensate (BEC) creates a new era in developing and designing principally novel types of quantum devices, including quantum sensors for measuring nonlinear interactions, external electrical and magnetic fields, and other physical characteristics with high sensitivity. Here we discuss the application of feedback control over a quantum sensor based on the Bose-Einstein condensate trapped in two dimensional ring potential. For a weakly interacting regime, the dynamics of such a system are modeled by three coupled complex differential master equations containing the parameter of interaction and the chemical potential parameter. The last one plays the role of control variable in sensing protocol for two body interaction. The goal of control is to minimize the effects of the higher energy levels in BEC by driving their corresponding matrix density elements. The control algorithm is designed as Kolesnikov’s feedback forming an artificial target attractor in the dynamical system. We re-formulate Kolesnikov’s approach in the operator form to adapt it to quantum engineering processes. The control approach proposed here can be efficiently extended to different sensing protocols for detecting external magnetic fields, rotational components, and other physical characteristics of BEC interacting with the environment.
Recent great progress in studying theoretical and especially experimental properties of BoseEinstein condensate (BEC) creates a new era in developing and designing principally novel types of quantum devices, including quantum sensors for measuring nonlinear interactions, external electrical and magnetic fields, and other physical characteristics with high sensitivity. Here we discuss the application of feedback control over a quantum sensor based on the Bose-Einstein condensate trapped in twodimensional ring potential. For a weakly interacting regime, the dynamics of such a system are modeled by three coupled complex differential master equations containing the parameter of interaction and the chemical potential parameter. The last one plays the role of control variable in sensing protocol for twobody interaction. The goal of control is to minimize the effects of the higher energy levels in BEC by driving their corresponding matrix density elements. The control algorithm is designed as Kolesnikov’s feedback forming an artificial target attractor in the dynamical system. We re-formulate Kolesnikov’s approach in the operator form to adapt it to quantum engineering processes. The control approach proposed here can be efficiently extended to different sensing protocols for detecting external magnetic fields, rotational components, and other physical characteristics of BEC interacting with the environment.
A quantum device for measuring two-body interactions, scalar magnetic fields and rotations is proposed using a Bose–Einstein condensate (BEC) in a ring trap. We consider an imbalanced superposition of orbital angular momentum modes with opposite winding numbers for which a rotating minimal atomic density line appears. We derive an analytical model relating the angular frequency of the minimal density line rotation to the strength of the nonlinear atom–atom interactions and the difference between the populations of the counter-propagating modes. Additionally, we propose a full experimental protocol based on direct fluorescence imaging of the BEC that allows to measure all the quantities involved in the analytical model and use the system for sensing purposes.
Weak measurement in tandem with real-time feedback control is a new route toward engineering novel nonequilibrium quantum matter. Here we develop a theoretical toolbox for quantum feedback control of multicomponent Bose-Einstein condensates (BECs) using backaction-limited weak measurements in conjunction with spatially resolved feedback. Feedback in the form of a single-particle potential can introduce effective interactions that enter into the stochastic equation governing system dynamics. The effective interactions are tunable and can be made analogous to Feshbach resonances-spin independent and spin dependent-but without changing atomic scattering parameters. Feedback cooling prevents runaway heating due to measurement backaction and we present an analytical model to explain its effectiveness. We showcase our toolbox by studying a two-component BEC using a stochastic mean-field theory, where feedback induces a phase transition between easy-axis ferromagnet and spin-disordered paramagnet phases. We present the steady-state phase diagram as a function of intrinsic and effective spin-dependent interaction strengths. Our result demonstrates that closed-loop quantum control of Bose-Einstein condensates is a powerful tool for quantum engineering in cold-atom systems.
Understanding and controlling many-body quantum systems in noisy environments is paramount to developing robust quantum technologies. An external environment can be thought of as a measurement reservoir which extracts information about the quantum system. Cold atoms are well suited to examine system-environment interaction via weak (i.e. minimally destructive) measurement techniques, wherein the measurement probe acts as the environment and also provides a noisy record of system dynamics. The measurement record can then be used in a feedback scheme, opening the door to real time control of quantum gases. In this talk I discuss our theoretical proposal to use weak measurement and feedback to engineer new phases in spin-1/2 Bose-Einstein condensates. We show that measurement and feedback alters the effective Hamiltonian governing system dynamics, thereby driving phase transitions reminiscent of a quantum quench for the closed system. We also develop a feedback cooling protocol which prevents runaway heating of the condensate due to measurement backaction. Our results show that measurement and feedback can alter condensate dynamics in a stable, controllable manner and provides a route toward Hamiltonian engineering in many-body systems. Finally, I will discuss ongoing experimental work to realize our proposal using Rb87.
Here we discuss as an important particular case the hybrid quantum electromagnetic sensor represented by a nitrogen-vacancy (NV) ensemble of N gt;gt; 1 centers in the doped diamond coupled to a high-quality factor dielectric resonator. The existing NV ensemble-based devices exhibit sensitivities that are several orders of magnitude away from theoretical limits. On the one hand, improvements in spin dephasing time, readout accuracy, and properties of the base diamond material can significantly improve the quality of operation of a quantum sensor. On the other hand, sensing optimization schemes also significantly affect its performance. We focus on the application of feedback to control the response in the cavity quantum electromagnetic sensor. We use the standard Tavis-Cummings model for the system and then introduce control over the target attractor method. In this model they are considered to be noninteracting two-level systems with transition frequencies wj, distributed inhomogeneously due to heterogeneous local magnetic and strain environments as well as hyperfine coupling with 14N nuclear spins. We adopted an operator form of closed-loop algorithm to the semi-classical Tavis-Cummings model in its ‘weak microwave drive’ limit. We used here target attractor Kolesnikov’s formulation of feedback to track the sensor response r or, alternatively, the reflected signal to the input drive field. In both cases, we achieve the tracking goal in the exponentially fast convergence.
Ultrasensitive quantum detection of external weak signals at the nanoscale levels can be implemented in a variety of forms. Here we discuss different feedback control algorithms for the sensing scenario based on the semiclassical Tavis-Cummings model for nitrogen-vacancy (NV) centers located in the diamond. In the frame of this model, the sensing elements are considered as non-interacting two-level quantum systems, distribute in-homogeneously due to heterogeneous local magnetic and strain environments. The dynamical system of ordinary differential equations corresponding to the model contains the set of control parameters: the detunings between the drive frequency and the cavity frequency and between the drive frequency and NV transition frequency, as well as the relaxation coefficients. Correspondingly, it opens a gate for developing feedback control algorithms for tracking the cavity field, the income signal, and the reflection signal in the model sensing system. To study the principal features of algorithmic feedback we formulate the simplified ’toy model’ for the Tavis-Cummings system and investigate alternative schemes of feedback (gradient methods, target attractor methods) to compare their pros and cons for effective control for nitrogen-vacancy-cavity quantum sensing based on different choices of the control parameter set. This work was supported by the Research Fund of Abdullah Gül University; Project Number: BAP FBA-2023-176 ’Geribesleme kontrol algoritmaları ile kubit tabanlı sensörlerin verimliliğinin artırılması’. The paper was presented at PhysCon2024.