Kater Murch

Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback

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. Here, we report the first implementation of quantum feedback control in a solid state system, in our case a superconducting quantum bit (qubit) coupled to a microwave cavity. Probing the state of the cavity with less than one photon on average, implements a weak measurement of the qubit state. These photons are then directed to a high-bandwidth quantum-noise-limited amplifier, which enables realtime monitoring of the state of the cavity—and hence that of the qubit—with high fidelity. We demonstrate quantum feedback control by inhibiting the decay of Rabi oscillations, allowing them to persist indefinitely. This new ability permits active suppression of decoherence and defines a path for continuous quantum error correction. Other novel avenues include quantum state stabilization, entanglement generation using measurement, state purification, and adaptive measurements.The act of measurement bridges the quantum and classical worlds by projecting a superposition of possible states into a single (probabilistic) outcome. The timescale of this ‘instantaneous’ process can be stretched using weak measurements, such 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. Here we implement quantum feedback control in a solid-state system, namely a superconducting quantum bit (qubit) coupled to a microwave cavity. A weak measurement of the qubit is implemented by probing the cavity with microwave photons, maintaining its average occupation at less than one photon. These photons are then directed to a high-bandwidth, quantum-noise-limited amplifier, which allows real-time monitoring of the state of the cavity (and, hence, that of the qubit) with high fidelity. We demonstrate quantum feedback control by inhibiting the decay of Rabi oscillations, allowing them to persist indefinitely. Such an ability permits the active suppression of decoherence and enables a method of quantum error correction based on weak continuous measurements. Other applications include quantum state stabilization, entanglement generation using measurement, state purification and adaptive measurements.

Cavity Nonlinear Optics at Low Photon Numbers from Collective Atomic Motion

We report on Kerr nonlinearity and dispersive optical bistability of a Fabry-Perot optical resonator due to the displacement of ultracold atoms trapped within. In the driven resonator, such collective motion is induced by optical forces acting upon up to 10(5) 87Rb atoms prepared in the lowest band of a one-dimensional intracavity optical lattice. The longevity of atomic motional coherence allows for strongly nonlinear optics at extremely low cavity photon numbers, as demonstrated by the observation of both branches of optical bistability at photon numbers below unity.

Observing single quantum trajectories of a superconducting quantum bit

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 state with 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’ determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories of the system. In this set-up, 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 the 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 foundation of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new means of implementing ‘quantum steering’—the harnessing of action at a distance to manipulate quantum states through measurement.

Bose-Einstein Condensation in a Circular Waveguide

We have produced Bose-Einstein condensates in a ring-shaped magnetic waveguide. The few-millimeter diameter, nonzero-bias ring is formed from a time-averaged quadrupole ring. Condensates that propagate around the ring make several revolutions within the time it takes for them to expand to fill the ring. The ring shape is ideally suited for studies of vorticity in a multiply connected geometry and is promising as a rotation sensor.

Cavity-Assisted Quantum Bath Engineering

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 state purity and effectively cools the dressed atom state to a low temperature.

Mapping the optimal route between two quantum states.

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. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance to chemical synthesis. A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories of a superconducting circuit that evolves under the competing influences of continuous weak measurement and Rabi drive. By tracking individual trajectories that evolve between any chosen initial and final states, we can deduce the most probable path through quantum state space. These pre- and post-selected quantum trajectories also reveal the optimal detector signal in the form of a smooth, time-continuous function that connects the desired boundary conditions. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wavefunction collapse, and unitary evolution of the quantum state as described by the Schrödinger equation. These results and the underlying theory, based on a principle of least action, reveal the optimal route from initial to final states, and may inform new quantum control methods for state steering and information processing.

Reduction of the radiative decay of atomic coherence in squeezed vacuum

Quantum fluctuations of the electromagnetic vacuum are responsible for physical effects such as the Casimir force and the radiative decay of atoms, and set fundamental limits on the sensitivity of measurements. Entanglement between photons can produce correlations that result in a reduction of these fluctuations below the ordinary vacuum level, allowing measurements that surpass the standard quantum limit in sensitivity. The effects of such ‘squeezed states’ of light on matter were first considered in a prediction of the radiative decay rates of atoms in squeezed vacuum. Despite efforts to demonstrate such effects in experiments with natural atoms, a direct quantitative observation of this prediction has remained elusive. Here we report a twofold reduction of the transverse radiative decay rate of a superconducting artificial atom coupled to continuum squeezed vacuum. The artificial atom is effectively a two-level system formed by the strong interaction between a superconducting circuit and a microwave-frequency cavity. A Josephson parametric amplifier is used to generate quadrature-squeezed electromagnetic vacuum. The observed twofold reduction in the decay rate of the atom allows the transverse coherence time, T2, to exceed the ordinary vacuum decay limit, 2T1. We demonstrate that the measured radiative decay dynamics can be used to reconstruct the Wigner distribution of the itinerant squeezed state. Our results confirm a canonical prediction of quantum optics and should enable new studies of the quantum light–matter interaction.

Single crystal silicon capacitors with low microwave loss in the single photon regime

We have fabricated superconducting microwave resonators in a lumped element geometry using single crystal silicon dielectric parallel plate capacitors with C>2 pF. Aluminum devices with resonant frequencies between 4.0 and 6.5 GHz exhibited an average internal quality factor Qi of 2×105 in the single photon excitation regime at T=20 mK. Attributing the observed loss solely to the capacitive element, our measurements place an upper bound on the loss tangent of the silicon dielectric layer of tan δi=5×10−6. This level of loss is an order of magnitude lower than is currently observed in structures incorporating amorphous dielectric materials, thus making single crystal silicon capacitors an attractive, robust route for realizing long-lived quantum circuits.

Prediction and retrodiction for a continuously monitored superconducting qubit.

The quantum state of a superconducting transmon qubit inside a three-dimensional cavity is monitored by transmission of a microwave field through the cavity. The information inferred from the measurement record is incorporated in a density matrix ρ_{t}, which is conditioned on probe results until t, and in an auxiliary matrix E_{t}, 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.

Collimated, single-pass atom source from a pulsed alkali metal dispenser for laser-cooling experiments

We have developed an improved scheme for loading atoms into a magneto-optical trap (MOT) from a directed rubidium alkali metal dispenser in <10−10Torr ultrahigh vacuum conditions. A current-driven dispenser was surrounded with a cold absorbing “shroud” held at ⩽0°C, pumping rubidium atoms not directed into the MOT. This nearly eliminates background atoms and reduces the detrimental rise in pressure normally associated with these devices. The system can be well-described as a current-controlled, rapidly switched, two-temperature thermal beam, and was used to load a MOT with 3×108atoms.