A qubit can relax by fluorescence, which prompts the release of a photon into its electromagnetic environment. By counting the emitted photons, discrete quantum jumps of the qubit state can be ...observed. The succession of states occupied by the qubit in a single experiment, its quantum trajectory, depends in fact on the kind of detector. How are the quantum trajectories modified if one measures continuously the amplitude of the fluorescence field instead? Using a superconducting parametric amplifier, we perform heterodyne detection of the fluorescence of a superconducting qubit. For each realization of the measurement record, we can reconstruct a different quantum trajectory for the qubit. The observed evolution obeys quantum state diffusion, which is characteristic of quantum measurements subject to zero-point fluctuations. Independent projective measurements of the qubit at various times provide a quantitative verification of the reconstructed trajectories. By exploring the statistics of quantum trajectories, we demonstrate that the qubit states span a deterministic surface in the Bloch sphere at each time in the evolution. Additionally, we show that when monitoring fluorescence field quadratures, coherent superpositions are generated during the decay from excited to ground state. Counterintuitively, measuring light emitted during relaxation can give rise to trajectories with increased excitation probability.
Symmetry-Preserving Observers Bonnabel, S.; Martin, P.; Rouchon, P.
IEEE transactions on automatic control,
12/2008, Letnik:
53, Številka:
11
Journal Article
Recenzirano
Odprti dostop
This paper presents the theory of invariant observers, i.e, symmetry-preserving observers. We consider an observer to consist of a copy of the system and a correction term, and we propose a ...constructive method (based on the Cartan moving-frame method) to find all the symmetry-preserving correction terms. The construction relies on an invariant frame (a classical notion) and on an invariant output-error, a less standard notion precisely defined here. Using the theory we build three non-linear observers for three examples of engineering interest: a non-holonomic car, a chemical reactor, and an inertial navigation system. For each example, the design is based on physical symmetries and the convergence analysis relies on the use of invariant state-errors, a symmetry-preserving way to define the estimation error.
In this technical note, we give a geometrical framework for the design of observers on finite-dimensional Lie groups for systems which possess some specific symmetries. The design and the error ...(between true and estimated state) equation are explicit and intrinsic. We consider also a particular case: left-invariant systems on Lie groups with right equivariant output. The theory yields a class of observers such that the error equation is autonomous. The observers converge locally around any trajectory, and the global behavior is independent from the trajectory, which is reminiscent of the linear stationary case.
Persistent control of a transmon qubit is performed by a feedback protocol based on continuous heterodyne measurement of its fluorescence. By driving the qubit and cavity with microwave signals whose ...amplitudes depend linearly on the instantaneous values of the quadratures of the measured fluorescence field, we show that it is possible to stabilize permanently the qubit in any targeted state. Using a Josephson mixer as a phase-preserving amplifier, it was possible to reach a total measurement efficiency η=35%, leading to a maximum of 59% of excitation and 44% of coherence for the stabilized states. The experiment demonstrates multiple-input multiple-output analog Markovian feedback in the quantum regime.
We propose an engineered reservoir inducing the relaxation of a cavity field towards nonclassical states. It is made up of two-level atoms crossing the cavity one at a time. Each atom-cavity ...interaction is first dispersive, then resonant, then dispersive again. The reservoir pointer states are those produced by an effective Kerr Hamiltonian acting on a coherent field. We thereby stabilize squeezed states and quantum superpositions of multiple coherent components in a cavity having a finite damping time. This robust decoherence protection method could be implemented in state-of-the-art experiments.
Rotor flux spatial position can be tracked in an ac machine even at low or zero stator frequency if a low-frequency harmonic current signal is injected into its stator. The harmonic current injection ...is source of the rotor speed perturbations which induce voltage oscillations in the stator winding at the injected frequency. By analyzing the stator winding voltage response, it is possible to detect the rotor flux position regardless of the stator frequency. This paper presents a stator current controller that is suitable for imposing rotating or pulsating harmonic current injection and a method for tracking the rotor flux position in either induction machines (IMs) or permanent-magnet synchronous machines (PMSMs). The controller contains, in addition to the standard fundamental-frequency-based synchronous reference frame (SRF) current controller, two sets of harmonic current integral controllers placed in respective harmonic SRFs. Such an extended current controller simultaneously performs two important tasks: controlled harmonic current injection with zero steady-state error and separation of particular spectral components in the stator voltage (spectral/sequence decomposition) which contain the rotor flux position information. The theoretical analysis presented, based on perturbation theory and averaging techniques, gives general expressions which link the rotor flux position error in IM and PMSM to the harmonic current controller outputs. Two special cases with the rotational and pulsating harmonic current injections are considered in more detail. The validity of the theoretical analysis and the feasibility of the sensorless rotor flux position detection are experimentally verified.
We consider an ensemble of quantum systems described by a density matrix, solution of a Lindblad-Kossakowski differential equation. We focus on the special case where the decoherence is only due to a ...highly unstable excited state and where the spontaneously emitted photons are measured by a photo-detector. We propose a systematic method to eliminate the fast and asymptotically stable dynamics associated with the excited state in order to obtain another differential equation for the slow part. We show that this slow differential equation is still of Lindblad-Kossakowski type, that the decoherence terms and the measured output depend explicitly on the amplitudes of quasi-resonant applied field, i.e., the control. Beside a rigorous proof of the slow/fast (adiabatic) reduction based on singular perturbation theory, we also provide a physical interpretation of the result in the context of coherence population trapping via dark states and decoherence-free subspaces. Numerical simulations illustrate the accuracy of the proposed approximation for a 5-level systems.
The efficient quantum state reconstruction algorithm described by Six et al. Phys. Rev. A 93, 012109 (2016)PLRAAN2469-992610.1103/PhysRevA.93.012109 is experimentally implemented on the nonlocal ...state of two microwave cavities entangled by a circular Rydberg atom. We use information provided by long sequences of measurements performed by resonant and dispersive probe atoms over timescales involving the system decoherence. Moreover, we benefit from the consolidation, in the same reconstruction, of different measurement protocols providing complementary information. Finally, we obtain realistic error bars for the matrix elements of the reconstructed density operator. These results demonstrate the pertinence and precision of the method, directly applicable to any complex quantum system.
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