Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session G18: Invited Session: Quantum Trajectories and State Estimation |
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Sponsoring Units: DCMP GQI Chair: Klaus Moelmer, Aarhus University, Denmark Room: Mission Room 103A |
Tuesday, March 3, 2015 11:15AM - 11:51AM |
G18.00001: Stochastic action principle approach to continuous quantum measurement Invited Speaker: Andrew Jordan New features in fundamental quantum physics appear in generalized (or weakened) measurements that are no longer simple projections. A sequence of weak measurements can also be made effectively continuous, producing monitored state evolution in the form of a quantum stochastic process. Previous theoretical investigations of this topic have mainly focused on using Langevin-type Stochastic Schrodinger equations to generate and study the quantum trajectories. Here, we reformulate the theory of continuous quantum measurement as a stochastic path integral, describing all possible quantum trajectories moving between initial and final quantum states. In order to do this, an auxiliary set of variables is introduced to impose the intrinsic state disturbance, doubling the state space of the system. The stochastic action encodes both the Hamiltonian and measurement dynamics. This formulation is well suited to finding the most-likely quantum path between chosen boundary conditions on the quantum states separated in time via a principle of least action. This action principle leads to a set of coupled nonlinear ordinary differential equations for the most likely path, structurally similar to Hamilton's equations. I will present predictions for the single and multiple qubit cases. Comparison to recent experiments with superconducting transmon qubits will be discussed. This formalism sheds new light on the conditional dynamics of monitored open quantum systems. [Preview Abstract] |
Tuesday, March 3, 2015 11:51AM - 12:27PM |
G18.00002: Ensembles of quantum trajectories-- a window into qubit measurement dynamics Invited Speaker: Steven Weber A central feature of quantum mechanics is that a measurement result is intrinsically probabilistic. Consequently, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. An accurate measurement record documents this stochastic evolution and can be used to reconstruct the quantum trajectory of the system state in a single experimental iteration. We use weak measurements to track the individual quantum trajectories of a superconducting qubit that evolves under the competing influences of continuous weak measurement and Rabi drive. We analyze large ensembles of such trajectories to examine their characteristics and to determine their statistical properties. For example, by considering only the subset of trajectories that evolve between any chosen initial and final states, we can deduce the most probably path through quantum state space. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wavefunction collapse, and unitary evolution. Our results provide insight into the dynamics of open quantum systems and may enable new methods of quantum state tomography, quantum state steering through measurement, and active quantum control. [Preview Abstract] |
Tuesday, March 3, 2015 12:27PM - 1:03PM |
G18.00003: Quantum State Smoothing Invited Speaker: Howard Wiseman Under noisy observations, one can estimate the state of the measured system, if its a priori statistics are given. In the continuous time situation, three different types of estimation can be distinguished: filtering, which is estimating of the state at time t from earlier records; retro-filtering, which is estimating it from later records; and smoothing, which is estimating it from both earlier and later records. Of the three, smoothing allows the greatest precision. Smoothing has been well developed in classical systems, but its application to quantum systems is very recent. Previous works have used the term ``quantum smoothing'' to mean estimating classical parameters, [Tsang, Phys. Rev. Lett 102, 250403 (2009); Yonezawa et al., Science 337, 1514-1517 (2012)]. This is essentially classical smoothing in which the noisy observation of the classical parameters is mediated by a quantum system. Here we introduce quantum state smoothing, where the state of a partially observed open quantum system itself is smoothed. We achieve this by applying classical smoothing to a hypothetical unobserved noisy measurement record that induces (in part) the stochastic dynamics (``quantum trajectories'') of the system. Using the formalism of linear quantum trajectories, we simulate quantum state smoothing for a qubit, and quantify how well it works. Our investigations shed new light on the nature of open quantum systems and the applicability of classical concepts. Applications to continuous measurement of solid-state qubits will be presented. [Preview Abstract] |
Tuesday, March 3, 2015 1:03PM - 1:39PM |
G18.00004: Unravelling quantum jumps by watching the fluorescence of a qubit Invited Speaker: Philippe Campagne-Ibarcq When the main source of qubit relaxation comes from its coupling to a photonic channel, each relaxation event is associated with the release of a photon. The corresponding discrete quantum jumps of the qubit state can be observed by counting the number of photons emitted by fluorescence. This discreteness of the quantum jumps is in fact related to the nature of the light detector. What does the evolution of the qubit state become if fluorescence is measured using a heterodyne detector instead? In this talk, an experiment will be discussed, in which the records of heterodyne measurements of fluorescence is used to reconstruct the quantum trajectories of a qubit during relaxation. Using a large number of experiments, it is shown that these trajectories can be used to better predict the probability to find given measurement outcomes during the evolution. This heterodyne measurement of the fluorescence is a quantum demolition continuous measurement, which is very different from the more common dispersive measurement sensitive to qubit occupation. These trajectories are thus expected to exhibit some exotic properties, particularly when using past and future knowledge. Besides, using measurement based feedback based on the fluorescence signal alone, it is possible to stabilize any chosen qubit state. This work thus demonstrates that relaxation into an efficiently monitored channel is not a limit for quantum information protocols but can instead be a resource. [Preview Abstract] |
Tuesday, March 3, 2015 1:39PM - 2:15PM |
G18.00005: Prediction, Retrodiction, and Smoothing for a Continuously Monitored Superconducting qubit Invited Speaker: Kater Murch The quantum state of a superconducting transmon qubit inside a three-dimensional cavity is monitored by reflection of a microwave field on the cavity. Measurement outcomes at different times are correlated, and knowledge of later measurement outcomes can be used to provide statistical information about earlier probe results. For a driven, damped and continuously monitored quantum system, the information inferred from measurement data yields a quantum trajectory given by the matrix $\rho_t$, which is conditioned on probe results until $t$. Further probing after the time $t$ can be incorporated into an auxiliary matrix $E_t$. We show that the combination of $\rho_t$ and $E_t$ makes nontrivially different and more precise predictions for the outcomes of measurements in the past. Our experiments verify the predictions of both projective and weak value (weak) measurements conditioned on full measurement records. [Preview Abstract] |
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