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The Journal of Chemical Physics

Quantum dynamics driven by continuous laser fields under measurements: Towards measurement-assisted quantum dynamics control

Michihiko Sugawara

Published Nov 22, 2005• 18 citations
Publisher

Abstract

We study quantum system dynamics driven by continuous laser fields under the measurement process. In order to take into account the system transition due to the measurement, we define the superoperator which eliminates the coherence relevant to the measured quantum states. We clarify that the dynamics of the measured states is frozen in the frequent measurement limit, while the space spanned by unmeasured states is isolated from the original system. We also derive the effective Liouvillian which governs incoherent population dynamics under the condition, in which measurements are frequently applied. We apply the formulation to two-level and Lambda-type three-level systems and clarify how the quantum measurements hinder the coherent population dynamics driven by the continuous laser fields in practical examples. Analysis on the laser field amplitude dependency of the final distribution in the t-->infinity limit suggests the possibility of the measurement-assisted quantum control.

DOI
10.1063/1.2132275

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We study quantum system dynamics driven by continuous laser fields under the measurement process. In order to take into account the system transition due to the measurement, we define the superoperator which eliminates the coherence relevant to the measured quantum states. We clarify that the dynamics of the measured states is frozen in the frequent measurement limit, while the space spanned by unmeasured states is isolated from the original system. We also derive the effective Liouvillian which governs incoherent population dynamics under the condition, in which measurements are frequently applied. We apply the formulation to two-level and Lambda-type three-level systems and clarify how the quantum measurements hinder the coherent population dynamics driven by the continuous laser fields in practical examples. Analysis on the laser field amplitude dependency of the final distribution in the t-->infinity limit suggests the possibility of the measurement-assisted quantum control.
Quantum measurements are considered for optimal control of quantum dynamics with instantaneous and continuous observations utilized to manipulate population transfer. With an optimal set of measurements, the highest yield in a two-level system can be obtained. An analytical solution is given for the problem of population transfer by measurement-assisted coherent control in a three-level system with dynamical symmetry. The anti-Zeno effect is recovered in the controlled processes. Demonstrations show that suitable observations can be powerful tools in the manipulation of quantum dynamics.
Wavefunction collapse is commonly associated with unavoidable physical disturbance of the measured system. Here we show that in driven-dissipative quantum systems, continuous measurement can induce strong trajectory-level collapse while leaving the ensemble-averaged steady state strictly invariant. We identify measurement-invariant steady states whose unconditional density matrix remains unchanged under continuous monitoring, despite pronounced measurement-induced localization in conditioned quantum trajectories. This separation between trajectory-level collapse and ensemble invariance defines a regime of partial collapse, in which measurement-induced localization is continuously counteracted by dissipative dynamics. We derive a necessary and sufficient condition for steady-state invariance under continuous measurement and identify Liouvillian symmetry as a concrete dynamical mechanism enforcing it. Our results clarify the distinction between conditional collapse and physical disturbance in open quantum systems and provide a framework for non-invasive continuous monitoring in driven-dissipative settings.
We propose the implementation of a strongly driven one-atom laser, based on the off-resonant interaction of a three-level atom in $\ensuremath{\Lambda}$ configuration with a single cavity mode and three laser fields. We show that the system can be described equivalently by a two-level atom resonantly coupled to the cavity and driven by a strong effective coherent field. The effective dynamics can be solved exactly, including a thermal field bath, allowing an analytical description of field statistics and entanglement properties. We also show the possible generation of quantum superposition (Schr\"odinger cat) states for the whole atom-field system and for the field alone after atomic measurement. We propose a way to monitor the system decoherence by measuring atomic populations. Finally, we confirm the validity of our model through numerical solutions.
A new quantum control scheme for general multilevel systems using intense laser fields is proposed. In the present scheme, the target subspace consisting of several quantum levels is effectively isolated by applying intense cw lasers with specific conditions. The formulation is carried out using the Green function with the help of projection operator method. Dynamics of the isolated target subspace is governed by an effective Hamiltonian. The developed scheme is applied to the quantum control of dissipative four- and five-level systems. It is clarified that the present method makes it possible not only to manipulate the coherent population dynamics but also to suppress the dissipative dynamics.
We present a theoretical investigation of a three-level Λ-type atom driven by a strong coherent laser and a weak stochastic field exhibiting amplitude and phase fluctuations. The stochastic field is modeled as a complex Gaussian–Markovian random process with finite bandwidth to describe realistic laser noise. Using the Born–Markov and rotating-wave approximations, we derive a Lindblad-form master equation that incorporates spontaneous emission and noise-induced terms, and we solve for the steady-state regime. We examine level populations in both the bare and dressed bases and compute the incoherent resonance-fluorescence spectrum. Our analysis shows that the stochastic drive is not merely a source of decoherence but a versatile control parameter. By detuning the stochastic-field central frequency relative to the coherent drive (especially for narrow bandwidths), we observe pronounced changes in emission characteristics, including selective enhancement or suppression, and reshaping of the multi-peaked fluorescence spectrum when the detuning matches the generalized Rabi frequency. Numerical results reveal nontrivial steady-state modifications distinct from purely coherent driving, enabling precise control of populations and suggesting applications in quantum control, quantum technologies, spectroscopy, and noise-assisted manipulation of atomic systems.
Abstract Quantum measurement has always been thought of as a formal, sudden projection that changes the system state instantly. However, in real life, the process of measurement involves a physical interaction that takes time to gather the information. The paper discusses the continuous quantum measurement that challenges the traditional instant measurement idea with the detector’s accumulated data continuously uninterruptedly. The paper starts by laying down the basic mathematics, which gradually leads to the modern Stochastic master equations and quantum trajectories through generalized measurements positive operator-valued measures and quantum instruments. The crucial experimental setups like circuit QED, trapped ions, and optomechanics are delineated where these notions have been put into practice. The significant ramifications of ongoing observation are then discussed, starting with the fundamental Zeno effect, measurement backaction, and continuing through the active steering of quantum states and the emergence of measurement-induced phase transitions in many-body systems. One of the main ideas of the paper is the attribute of measurement as a powerful control method which enables real-time feedback, state stabilization, and continuous quantum error correction. Finally, the paper points out the open problems that remain in the areas of many-body systems’ scalability and the coupling of machine learning with real-time quantum control.