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Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as by an ideal photodetector. Here we derive (non-Markovian) quantum trajectories for realistic photodetection, including the effects of efficiency, dead time, bandwidth, electronic noise, and dark counts. We apply our theory to a realistic cavity QED scenario and investigate the impact of such detector imperfections on the conditional evolution of the system state. A practical theory of quantum trajectories with realistic detection will be essential for experimental and technological applications of quantum feedback in many areas.
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We employ a quantum trajectory approach to characterize synchronization and phase-locking between open quantum systems in nonequilibrium steady states. We exemplify our proposal for the paradigmatic case of two quantum Van der Pol oscillators interacting through dissipative coupling. We show the deep impact of synchronization on the statistics of phase-locking indicators and other correlation measures defined for single trajectories, spotting a link between the presence of synchronization and the emergence of large tails in the probability distribution for the entanglement along trajectories. Our results shed new light on fundamental issues regarding quantum synchronization providing new methods for its precise quantification.
We consider the quantum (trajectories) filtering equation for the case when the system is driven by Bose field inputs prepared in an arbitrary non-zero mean Gaussian state. The a posteriori evolution of the system is conditioned by the results of a single or double homodyne measurements. The system interacting with the Bose field is a single cavity mode taken initially in a Gaussian state. We show explicit solutions using the method of characteristic functions to the filtering equations exploiting the linear Gaussian nature of the problem.
In this review, we discuss recent experiments that investigate how the quantum sate of a superconducting qubit evolves during measurement. We provide a pedagogical overview of the measurement process, when the qubit is dispersively coupled to a microwave frequency cavity, and the qubit state is encoded in the phase of a microwave tone that probes the cavity. A continuous measurement record is used to reconstruct the individual quantum trajectories of the qubit state, and quantum state tomography is performed to verify that the state has been tracked accurately. Furthermore, we discuss ensembles of trajectories, time-symmetric evolution, two-qubit trajectories, and potential applications in measurement-based quantum error correction.
The computational cost of preparing a quantum state can be substantial depending on the structure of data to be encoded. Many quantum algorithms require repeated sampling to find the answer, mandating reconstruction of the same input state for every execution of an algorithm. Thus, the advantage of quantum computation can diminish due to redundant state initialization. We present a framework based on quantum forking that bypasses this fundamental issue and expedites a family of tasks that require sampling from independent quantum processes. Quantum forking propagates an input state to multiple quantum trajectories in superposition, and a weighted power sum of individual results from each trajectories is obtained in one measurement via quantum interference. The significance of our work is demonstrated via applications to implementing non-unitary quantum channels, studying entanglement and benchmarking quantum control. A proof-of-principle experiment is implemented on the IBM and Rigetti quantum cloud platforms.
The interaction between matter and squeezed light has mostly been treated within the approximation that the field correlation time is small. Methods for treating squeezed light with more general correlations currently involve explicitly modeling the systems producing the light. We develop a general purpose input-output theory for a particular form of narrowband squeezed light -- a squeezed wave-packet mode -- that only cares about the statistics of the squeezed field and the shape of the wave packet. This formalism allows us to derive the input-output relations and the master equation. We also consider detecting the scattered field using photon counting and homodyne measurements which necessitates the derivation of the stochastic master equation. The non Markovian nature of the field manifests itself in the master equation as a coupled hierarchy of equations. We illustrate these with consequences for the decay and resonance fluorescence of two-level atoms in the presence of such fields.
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