Open systems with gain and loss, described by non-Hermitian Hamiltonians, have been a subject of intense research recently. In classical systems, the effect of exceptional-point degeneracieson their dynamics has been observed through remarkable phenomena such as the parity-time symmetry breaking transition, asymmetric mode switching, and optimal energy transfer. On the other hand, consequences of an exceptional point for quantum evolution and decoherence are hitherto unexplored. Here, we use post-selection on a three-level superconducting transmon circuit with tunable Rabi drive, dissipation, and detuning to carry out quantum state tomography of a single dissipative qubit in the vicinity of its exceptional point. Quantum state tomography reveals the PT symmetry breaking transition at zero detuning, decoherence enhancement at finite detuning, and a quantum signature of the exceptional point in the qubit relaxation state. Our observations demonstrate rich phenomena associated with non-Hermitian physics in the fully quantum regime and open routes to explore and harness exceptional point degeneracies for enhanced sensing and quantum information processing.
A quantum emitter decays due to vacuum fluctuations at its transition frequency. By virtue of the entwined nature of dissipation and fluctuations, this process can be controlled byengineering the impedance of the environment. We study how the structured vacuum environment of a microwave photonic crystal can be used for bath engineering of a transmon qubit. The photonic crystal is realized by a step-impedance transmission line which suppresses and enhances the quantum spectral density of states akin to a Purcell filter. We demonstrate a bath engineering protocol upon driving an emitter near the photonic band edge that allows dissipation to produce non-trivial steady-states.
In both thermodynamics and quantum mechanics the arrow of time is characterized by the statistical likelihood of physical processes. We characterize this arrow of time for the continuousquantum measurement dynamics of a superconducting qubit. By experimentally tracking individual weak measurement trajectories, we compare the path probabilities of forward and backward-in-time evolution to develop an arrow of time statistic associated with measurement dynamics. We compare the statistics of individual trajectories to ensemble properties showing that the measurement dynamics obeys both detailed and integral fluctuation theorems thus establishing the consistency between microscopic and macroscopic measurement dynamics.
Precision measurements of frequency are critical to accurate timekeeping, and are fundamentally limited by quantum measurement uncertainties. While for time-independent quantum Hamiltonians,the uncertainty of any parameter scales at best as 1/T, where T is the duration of the experiment, recent theoretical works have predicted that explicitly time-dependent Hamiltonians can yield a 1/T2 scaling of the uncertainty for an oscillation frequency. This quantum acceleration in precision requires coherent control, which is generally adaptive. We experimentally realize this quantum improvement in frequency sensitivity with superconducting circuits, using a single transmon qubit. With optimal control pulses, the theoretically ideal frequency precision scaling is reached for times shorter than the decoherence time. This result demonstrates a fundamental quantum advantage for frequency estimation.
We use a near-quantum-limited detector to experimentally track individual quantum trajectories of a driven qubit formed by the hybridization of a waveguide cavity and a transmon circuit.For each measured quantum coherent trajectory, we separately identify energy changes of the qubit as heat and work, and verify the first law of thermodynamics for an open quantum system. We further employ a novel quantum feedback loop to compensate for the exchanged heat and effectively isolate the qubit. By verifying the Jarzynski equality for the distribution of applied work, we demonstrate the validity of the second law of thermodynamics. Our results establish thermodynamics along individual quantum trajectories.
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.