304 research outputs found
Quantum smoothing for classical mixtures
In quantum mechanics, wave functions and density matrices represent our
knowledge about a quantum system and give probabilities for the outcomes of
measurements. If the combined dynamics and measurements on a system lead to a
density matrix with only diagonal elements in a given basis
, it may be treated as a classical mixture, i.e., a system which
randomly occupies the basis states with probabilities
. Fully equivalent to so-called smoothing in classical
probability theory, subsequent probing of the occupation of the states
improves our ability to retrodict what was the outcome of a
projective state measurement at time . Here, we show with experiments on a
superconducting qubit that the smoothed probabilities do not, in the same way
as the diagonal elements of , permit a classical mixture interpretation
of the state of the system at the past time .Comment: 5 pages, 4 figure
Achieving optimal quantum acceleration of frequency estimation using adaptive coherent control
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 , where is the duration of the experiment, recent
theoretical works have predicted that explicitly time-dependent Hamiltonians
can yield a 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.Comment: 8 pages, 4 figure
Quantum Zeno effects from measurement controlled qubit-bath interactions
The Zeno and anti-Zeno effects are features of measurement-driven quantum
evolution where frequent measurement inhibits or accelerates the decay of a
quantum state. Either type of evolution can emerge depending on the
system-environment interaction and measurement method. In this experiment, we
use a superconducting qubit to map out both types of Zeno effect in the
presence of structured noise baths and variable measurement rates. We observe
both the suppression and acceleration of qubit decay as repeated measurements
are used to modulate the qubit spectrum causing the qubit to sample different
portions of the bath. We compare the Zeno effects arising from dispersive
energy measurements and purely-dephasing `quasi'-measurements, showing energy
measurements are not necessary to accelerate or suppress the decay process.Comment: 7 pages, 8 figure
Correlations of the time dependent signal and the state of a continuously monitored quantum system
In quantum physics, measurements give random results and yield a
corresponding random back action on the state of the system subject to
measurement. If a quantum system is probed continuously over time, its state
evolves along a stochastic quantum trajectory. To investigate the
characteristic properties of such dynamics, we perform weak continuous
measurements on a superconducting qubit that is driven to undergo Rabi
oscillations. From the data we observe a number of striking temporal
correlations within the time dependent signals and the quantum trajectories of
the qubit, and we discuss their explanation in terms of quantum measurement and
photodetection theory.Comment: 8 pages 5 figure
Observing single quantum trajectories of a superconducting qubit
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 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.Comment: 7 pages, 6 figure
Bath engineering of a fluorescing artificial atom with a photonic crystal
We demonstrate how the dissipative interaction between a superconducting
qubit and a microwave photonic crystal can be used for quantum bath
engineering. The photonic crystal is created with a step-impedance transmission
line which suppresses and enhances the quantum spectral density of states,
influencing decay transitions of a transmon circuit. The qubit interacts with
the transmission line indirectly via dispersive coupling to a cavity. We
characterize the photonic crystal density of states from both the unitary and
dissipative dynamics of the qubit. When the qubit is driven, it dissipates into
the frequency dependent density of states of the photonic crystal. Our result
is the deterministic preparation of qubit superposition states as the
steady-state of coherent driving and dissipation near by the photonic crystal
band edge, which we characterize with quantum state tomography. Our results
highlight how the multimode environment from the photonic crystal forms a
resource for quantum control.Comment: 9 pages 7 figure
Mapping quantum state dynamics in spontaneous emission
The evolution of a quantum state undergoing radiative decay depends on how
the emission is detected. We employ phase-sensitive amplification to perform
homodyne detection of the spontaneous emission from a superconducting
artificial atom. Using quantum state tomography, we characterize the
correlation between the detected homodyne signal and the emitter's state, and
map out the conditional back-action of homodyne measurement. By tracking the
diffusive quantum trajectories of the state as it decays, we characterize
selective stochastic excitation induced by the choice of measurement basis. Our
results demonstrate dramatic differences from the quantum jump evolution that
is associated with photodetection and highlight how continuous field detection
can be harnessed to control quantum evolution.Comment: 8 pages, 8 figure
Suppression 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 vacuum level allowing measurements that surpass the
standard quantum limit in sensitivity. Here we demonstrate that the radiative
decay rate of an atom that is coupled to quadrature squeezed electromagnetic
vacuum can be reduced below its natural linewidth. We observe a two-fold
reduction of the transverse radiative decay rate of a superconducting
artificial atom coupled to continuum squeezed vacuum generated by a Josephson
parametric amplifier, allowing the transverse coherence time T_2 to exceed the
vacuum decay limit of 2T_1. We demonstrate that the measured radiative decay
dynamics can be used to tomographically reconstruct the Wigner distribution of
the the itinerant squeezed state. Our results are the first confirmation of a
canonical prediction of quantum optics and open the door to new studies of the
quantum light-matter interaction.Comment: 9 pages, 5 figure
Homodyne monitoring of post-selected decay
We use homodyne detection to monitor the radiative decay of a superconducting
qubit. According to the classical theory of conditional probabilities, the
excited state population differs from an exponential decay law if it is
conditioned upon a later projective qubit measurement. Quantum trajectory
theory accounts for the expectation values of general observables, and we use
experimental data to show how a homodyne detection signal is conditioned upon
both the initial state and the finally projected state of a decaying qubit. We
observe, in particular, how anomalous weak values occur in continuous weak
measurement for certain pre- and post-selected states. Subject to homodyne
detection, the density matrix evolves in a stochastic manner, but it is
restricted to a specific surface in the Bloch sphere. We show that a similar
restriction applies to the information associated with the post-selection, and
thus bounds the predictions of the theory.Comment: 11 pages, 8 figure
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 Q_i of 2 x 10^5 in the single
photon excitation regime at T = 20 mK. Attributing all the observed loss to the
capacitive element, our measurements correspond to a loss tangent of intrinsic
silicon of 5 x 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
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