37 research outputs found
Feedback generation of quantum Fock states by discrete QND measures
A feedback scheme for preparation of photon number states in a microwave
cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity
field provides information on its actual state. The control consists in
injecting into the cavity mode a microwave pulse adjusted to maximize the
population of the desired target photon number. In the ideal case (perfect
cavity and measures), we present the feedback scheme and its detailed
convergence proof through stochastic Lyapunov techniques based on
super-martingales and other probabilistic arguments. Quantum Monte-Carlo
simulations performed with experimental parameters illustrate convergence and
robustness of such feedback scheme.Comment: submitted, update version with feedback law of arXiv:0905.0114
[quant-ph
Single atoms on demand for cavity QED experiments
Cavity quantum electrodynamics (cavity QED) describes electromagnetic fields in a confined space and the radiative properties of atoms in such fields. The simplest example of such system is a single atom interacting with one mode of a high-finesse resonator. Besides observation and exploration of fundamental quantum mechanical effects, this system bears a high potential for applications quantum information science such as, e.g., quantum logic gates, quantum communication and quantum teleportation. In this thesis I present an experiment on the deterministic coupling of a single neutral atom to the mode of a high-finesse optical resonator. In Chapter 1 I describe our basic techniques for trapping and observing single cesium atoms. As a source of single atoms we use a high-gradient magneto-optical trap, which captures the atoms from background gas in a vacuum chamber and cools them down to millikelvin temperatures. The atoms are then transferred without loss into a standing-wave dipole trap, which provides a conservative potential required for experiments on atomic coherence such as quantum information processing and metrology on trapped atoms. Moreover, shifting the standing-wave pattern allows us to deterministically transport the atoms (Chapter 2). In combination with non-destructive fluorescence imaging of individual trapped atoms, this enables us to control their position with submicrometer precision over several millimeters along the dipole trap. The cavity QED system can distinctly display quantum behaviour in the so-called strong coupling regime, i.e., when the coherent atom-cavity coupling rate dominates dissipation in the system. This sets the main requirements on the resonator's properties: small mode volume and high finesse. Chapter 3 is devoted to the manufacturing, assembling, and testing of an ultra-high finesse optical Fabry-Perot resonator, stabilized to the atomic transition. In Chapter 4 I present the transportation of single atoms into the cavity and their coupling to the cavity mode. The strong coupling manifests itself in a strong reduction of the cavity transmission probed by a weak external laser. The atoms remain trapped and coupled to the cavity mode for several seconds until we move them out of the cavity for final analysis of their number and position
Quantum state tomography with non-instantaneous measurements, imperfections and decoherence
Tomography of a quantum state is usually based on positive operator-valued
measure (POVM) and on their experimental statistics. Among the available
reconstructions, the maximum-likelihood (MaxLike) technique is an efficient
one. We propose an extension of this technique when the measurement process
cannot be simply described by an instantaneous POVM. Instead, the tomography
relies on a set of quantum trajectories and their measurement records. This
model includes the fact that, in practice, each measurement could be corrupted
by imperfections and decoherence, and could also be associated with the record
of continuous-time signals over a finite amount of time. The goal is then to
retrieve the quantum state that was present at the start of this measurement
process. The proposed extension relies on an explicit expression of the
likelihood function via the effective matrices appearing in quantum smoothing
and solutions of the adjoint quantum filter. It allows to retrieve the initial
quantum state as in standard MaxLike tomography, but where the traditional POVM
operators are replaced by more general ones that depend on the measurement
record of each trajectory. It also provides, aside the MaxLike estimate of the
quantum state, confidence intervals for any observable. Such confidence
intervals are derived, as the MaxLike estimate, from an asymptotic expansion of
multi-dimensional Laplace integrals appearing in Bayesian Mean estimation. A
validation is performed on two sets of experimental data: photon(s) trapped in
a microwave cavity subject to quantum non-demolition measurements relying on
Rydberg atoms; heterodyne fluorescence measurements of a superconducting qubit.Comment: 11 pages, 4 figures, submitte
Design and Stability of Discrete-Time Quantum Filters with Measurement Imperfections
This work considers the theory underlying a discrete-time quantum filter
recently used in a quantum feedback experiment. It proves that this filter
taking into account decoherence and measurement errors is optimal and stable.
We present the general framework underlying this filter and show that it
corresponds to a recursive expression of the least-square optimal estimation of
the density operator in the presence of measurement imperfections. By
measurement imperfections, we mean in a very general sense unread measurement
performed by the environment (decoherence) and active measurement performed by
non-ideal detectors. However, we assume to know precisely all the Kraus
operators and also the detection error rates. Such recursive expressions
combine well known methods from quantum filtering theory and classical
probability theory (Bayes' law). We then demonstrate that such a recursive
filter is always stable with respect to its initial condition: the fidelity
between the optimal filter state (when the initial filter state coincides with
the real quantum state) and the filter state (when the initial filter state is
arbitrary) is a sub-martingale.Comment: Submitted to the American Control Conference 201
Alternative experimental ways to access entropy production
We theoretically derive and experimentally compare several different ways to
access entropy production in a quantum process under feedback control. We focus
on a bipartite quantum system realizing an autonomous Maxwell's demon scheme
reported by Najera-Santos et al. [Phys.~Rev.~Research 2, 032025(R) (2020)],
where information encoded in a demon is consumed to transfer heat from a cold
qubit to a hot cavity. By measuring individual quantum trajectories of the
joint demon-cavity-qubit system, we compute the entropy production with six
distinct expressions derived from different approaches to the system
description and its evolution. Each method uses a specific set of trajectories
and data processing. Our results provide a unified view on the various meanings
of irreversibility in quantum systems and pave the way to the measurement of
entropy production beyond thermal frameworks.Comment: 15 pages, 10 figure
Real-time quantum feedback prepares and stabilizes photon number states
Feedback loops are at the heart of most classical control procedures. A
controller compares the signal measured by a sensor with the target value. It
adjusts then an actuator in order to stabilize the signal towards its target.
Generalizing this scheme to stabilize a micro-system's quantum state relies on
quantum feedback, which must overcome a fundamental difficulty: the
measurements by the sensor have a random back-action on the system. An optimal
compromise employs weak measurements providing partial information with minimal
perturbation. The controller should include the effect of this perturbation in
the computation of the actuator's unitary operation bringing the incrementally
perturbed state closer to the target. While some aspects of this scenario have
been experimentally demonstrated for the control of quantum or classical
micro-system variables, continuous feedback loop operations permanently
stabilizing quantum systems around a target state have not yet been realized.
We have implemented such a real-time stabilizing quantum feedback scheme. It
prepares on demand photon number states (Fock states) of a microwave field in a
superconducting cavity and subsequently reverses the effects of
decoherence-induced field quantum jumps. The sensor is a beam of atoms crossing
the cavity which repeatedly performs weak quantum non-demolition measurements
of the photon number. The controller is implemented in a real-time computer
commanding the injection, between measurements, of adjusted small classical
fields in the cavity. The microwave field is a quantum oscillator usable as a
quantum memory or as a quantum bus swapping information between atoms. By
demonstrating that active control can generate non-classical states of this
oscillator and combat their decoherence, this experiment is a significant step
towards the implementation of complex quantum information operations.Comment: 12 pages, 4 figure
Towards quantum simulation with circular Rydberg atoms
The main objective of quantum simulation is an in-depth understanding of
many-body physics. It is important for fundamental issues (quantum phase
transitions, transport, . . . ) and for the development of innovative
materials. Analytic approaches to many-body systems are limited and the huge
size of their Hilbert space makes numerical simulations on classical computers
intractable. A quantum simulator avoids these limitations by transcribing the
system of interest into another, with the same dynamics but with interaction
parameters under control and with experimental access to all relevant
observables. Quantum simulation of spin systems is being explored with trapped
ions, neutral atoms and superconducting devices. We propose here a new paradigm
for quantum simulation of spin-1/2 arrays providing unprecedented flexibility
and allowing one to explore domains beyond the reach of other platforms. It is
based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes
combined with the inhibition of their microwave spontaneous emission and their
low sensitivity to collisions and photoionization make trapping lifetimes in
the minute range realistic with state-of-the-art techniques. Ultra-cold
defect-free circular atom chains can be prepared by a variant of the
evaporative cooling method. This method also leads to the individual detection
of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2
Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz.
All the model parameters can be tuned at will, making a large range of
simulations accessible. The system evolution can be followed over times in the
range of seconds, long enough to be relevant for ground-state adiabatic
preparation and for the study of thermalization, disorder or Floquet time
crystals. This platform presents unrivaled features for quantum simulation