We employ phase-sensitive amplification to perform homodyne detection of the resonance fluorescence from a driven superconducting artificial atom. Entanglement between the emitter andits fluorescence allows us to track the individual quantum state trajectories of the emitter conditioned on the outcomes of the field measurements. We analyze the ensemble properties of these trajectories by considering trajectories that connect specific initial and final states. By applying the stochastic path integral formalism, we calculate equations-of-motion for the most likely path between two quantum states and compare these predicted paths to experimental data. Drawing on the mathematical similarity between the action formalism of the most likely quantum paths and ray optics we study the emergence of caustics in quantum trajectories – places where multiple extrema in the stochastic action occur. We observe such multiple most likely paths in experimental data and find these paths to be in reasonable quantitative agreement with theoretical calculations.
A superconducting transmon qubit undergoing driven unitary evolution is continuously monitored to observe the time evolution of its quantum state. If projective measurements are usedto herald a definite initial state, the average of many measurement records displays damped Rabi oscillations. If instead the average of many measurements is conditioned on the outcome of a final post-selection measurement, the result exhibits similar damped Rabi oscillations with the exception that the damping of the signal occurs backwards in time. Such pre- and post-selections are specific examples of qubit state and signal temporal correlations and stimulate a more general discussion of the temporal correlations in stochastic quantum trajectories associated with continuous quantum measurements.
We describe the implementation of weak quantum measurements in superconducting qubits, focusing specifically on transmon type devices in the circuit quantum electrodynamics architecture.To access this regime, the readout cavity is probed with on average a single microwave photon. Such low-level signals are detected using near quantum-noise-limited superconducting parametric amplifiers. Weak measurements yield partial information about the quantum state, and correspondingly do not completely project the qubit into an eigenstate. As such, we use the measurement record to either sequentially reconstruct the quantum state at a given time, yielding a quantum trajectory, or to close a direct quantum feedback loop, stabilizing Rabi oscillations indefinitely.
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 measurementprocess, 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 quantum state of a superconducting transmon qubit inside a three-dimensional cavity is monitored by reflection of a microwave field on the cavity. The information inferred fromthe measurement record is incorporated in a density matrix ρt, which is conditioned on probe results until t, and in an auxiliary matrix Et, which is conditioned on probe results obtained after t. Here, we obtain these matrices from experimental data and we illustrate their application to predict and retrodict the outcome of weak and strong qubit measurements.
The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum statewith the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture-a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a quantum trajectory conditioned on the measurement outcome. We employ weak measurements to monitor a microwave cavity embedding a superconducting qubit and track the individual quantum trajectories of the system. In this architecture, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring and validate the foundations of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new route for implementing what Schrodinger termed „quantum steering“-harnessing action at a distance to manipulate quantum states via measurement.
When a frequency chirped excitation is applied to a classical high-Q
nonlinear oscillator, its motion becomes dynamically synchronized to the drive
and large oscillation amplitude isobserved, provided the drive strength
exceeds the critical threshold for autoresonance. We demonstrate that when such
an oscillator is strongly coupled to a quantized superconducting qubit, both
the effective nonlinearity and the threshold become a non-trivial function of
the qubit-oscillator detuning. Moreover, the autoresonant threshold is
sensitive to the quantum state of the qubit and may be used to realize a high
fidelity, latching readout whose speed is not limited by the oscillator Q.
We demonstrate quantum bath engineering for a superconducting artificial atom
coupled to a microwave cavity. By tailoring the spectrum of microwave photon
shot noise in the cavity,we create a dissipative environment that autonomously
relaxes the atom to an arbitrarily specified coherent superposition of the
ground and excited states. In the presence of background thermal excitations,
this mechanism increases the state purity and effectively cools the dressed
atom state to a low temperature.
The act of measurement bridges the quantum and classical worlds by projecting
a superposition of possible states into a single, albeit probabilistic,
outcome. The time-scale of this„instantaneous“ process can be stretched using
weak measurements so that it takes the form of a gradual random walk towards a
final state. Remarkably, the interim measurement record is sufficient to
continuously track and steer the quantum state using feedback. We monitor the
dynamics of a resonantly driven quantum two-level system — a superconducting
quantum bit –using a near-noiseless parametric amplifier. The high-fidelity
measurement output is used to actively stabilize the phase of Rabi
oscillations, enabling them to persist indefinitely. This new functionality
shows promise for fighting decoherence and defines a path for continuous
quantum error correction.