75 research outputs found
Single microwave photon detection in the micromaser
High efficiency single photon detection is an interesting problem for many
areas of physics, including low temperature measurement, quantum information
science and particle physics. For optical photons, there are many examples of
devices capable of detecting single photons with high efficiency. However
reliable single photon detection of microwaves is very difficult, principally
due to their low energy. In this paper we present the theory of a cascade
amplifier operating in the microwave regime that has an optimal quantum
efficiency of 93%. The device uses a microwave photon to trigger the stimulated
emission of a sequence of atoms where the energy transition is readily
detectable. A detailed description of the detector's operation and some
discussion of the potential limitations of the detector are presented.Comment: 8 pages, 5 figure
Jump-like unravelings for non-Markovian open quantum systems
Non-Markovian evolution of an open quantum system can be `unraveled' into
pure state trajectories generated by a non-Markovian stochastic (diffusive)
Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently
we have shown that such equations can be derived using the modal (hidden
variable) interpretation of quantum mechanics. In this paper we generalize this
theory to treat jump-like unravelings. To illustrate the jump-like behavior we
consider a simple system: A classically driven (at Rabi frequency )
two-level atom coupled linearly to a three mode optical bath, with a central
frequency equal to the frequency of the atom, , and the two side
bands have frequencies . In the large limit we
observed that the jump-like behavior is similar to that observed in this system
with a Markovian (broad band) bath. This is expected as in the Markovian limit
the fluorescence spectrum for a strongly driven two level atom takes the form
of a Mollow triplet. However the length of time for which the Markovian-like
behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure
Detection statistics in the micromaser
We present a general method for the derivation of various statistical
quantities describing the detection of a beam of atoms emerging from a
micromaser. The user of non-normalized conditioned density operators and a
linear master equation for the dynamics between detection events is discussed
as are the counting statistics, sequence statistics, and waiting time
statistics. In particular, we derive expressions for the mean number of
successive detections of atoms in one of any two orthogonal states of the
two-level atom. We also derive expressions for the mean waiting times between
detections. We show that the mean waiting times between de- tections of atoms
in like states are equivalent to the mean waiting times calculated from the
uncorrelated steady state detection rates, though like atoms are indeed
correlated. The mean waiting times between detections of atoms in unlike states
exhibit correlations. We evaluate the expressions for various detector
efficiencies using numerical integration, reporting re- sults for the standard
micromaser arrangement in which the cavity is pumped by excited atoms and the
excitation levels of the emerging atoms are measured. In addition, the atomic
inversion and the Fano-Mandel function for the detection of de-excited atoms is
calculated for compari- son to the recent experimental results of Weidinger et
al. [1], which reports the first observation of trapping states.Comment: 26 pages, 11 figure
Physical interpretation of stochastic Schroedinger equations in cavity QED
We propose physical interpretations for stochastic methods which have been
developed recently to describe the evolution of a quantum system interacting
with a reservoir. As opposed to the usual reduced density operator approach,
which refers to ensemble averages, these methods deal with the dynamics of
single realizations, and involve the solution of stochastic Schr\"odinger
equations. These procedures have been shown to be completely equivalent to the
master equation approach when ensemble averages are taken over many
realizations. We show that these techniques are not only convenient
mathematical tools for dissipative systems, but may actually correspond to
concrete physical processes, for any temperature of the reservoir. We consider
a mode of the electromagnetic field in a cavity interacting with a beam of two-
or three-level atoms, the field mode playing the role of a small system and the
atomic beam standing for a reservoir at finite temperature, the interaction
between them being given by the Jaynes-Cummings model. We show that the
evolution of the field states, under continuous monitoring of the state of the
atoms which leave the cavity, can be described in terms of either the Monte
Carlo Wave-Function (quantum jump) method or a stochastic Schr\"odinger
equation, depending on the system configuration. We also show that the Monte
Carlo Wave-Function approach leads, for finite temperatures, to localization
into jumping Fock states, while the diffusion equation method leads to
localization into states with a diffusing average photon number, which for
sufficiently small temperatures are close approximations to mildly squeezed
states.Comment: 12 pages RevTeX 3.0 + 6 figures (GIF format; for higher-resolution
postscript images or hardcopies contact the authors.) Submitted to Phys. Rev.
Resonance fluorescence in a band gap material: Direct numerical simulation of non-Markovian evolution
A numerical method of calculating the non-Markovian evolution of a driven
atom radiating into a structured continuum is developed. The formal solution
for the atomic reduced density matrix is written as a Markovian algorithm by
introducing a set of additional, virtual density matrices which follow, to the
level of approximation of the algorithm, all the possible trajectories of the
photons in the electromagnetic field. The technique is perturbative in the
sense that more virtual density matrices are required as the product of the
effective memory time and the effective coupling strength become larger. The
number of density matrices required is given by where is the number
of timesteps per memory time. The technique is applied to the problem of a
driven two-level atom radiating close to a photonic band gap and the
steady-state correlation function of the atom is calculated.Comment: 14 pages, 9 figure
Driving the atom by atomic fluorescence: analytic results for the power and noise spectra
We study how the spectral properties of resonance fluorescence propagate
through a two-atom system. Within the weak-driving-field approximation we find
that, as we go from one atom to the next, the power spectrum exhibits both
sub-natural linewidth narrowing and large asymmetries while the spectrum of
squeezing narrows but remains otherwise unchanged. Analytical results for the
observed spectral features of the fluorescence are provided and their origin is
thoroughly discussed.Comment: 13 pages, 5 figures; to be published in Phys. Rev. A Changed title
and conten
Frontiers of open quantum system dynamics
We briefly examine recent developments in the field of open quantum system
theory, devoted to the introduction of a satisfactory notion of memory for a
quantum dynamics. In particular, we will consider a possible formalization of
the notion of non-Markovian dynamics, as well as the construction of quantum
evolution equations featuring a memory kernel. Connections will be drawn to the
corresponding notions in the framework of classical stochastic processes, thus
pointing to the key differences between a quantum and classical formalization
of the notion of memory effects.Comment: 15 pages, contribution to "Quantum Physics and Geometry", Lecture
Notes of the Unione Matematica Italiana 25,E. Ballico et al. (eds.
Non-Markovian quantum trajectories for spectral detection
We present a formulation of non-Markovian quantum trajectories for open
systems from a measurement theory perspective. In our treatment there are three
distinct ways in which non-Markovian behavior can arise; a mode dependent
coupling between bath (reservoir) and system, a dispersive bath, and by
spectral detection of the output into the bath. In the first two cases the
non-Markovian behavior is intrinsic to the interaction, in the third case the
non-Markovian behavior arises from the method of detection. We focus in detail
on the trajectories which simulate real-time spectral detection of the light
emitted from a localized system. In this case, the non-Markovian behavior
arises from the uncertainty in the time of emission of particles that are later
detected. The results of computer simulations of the spectral detection of the
spontaneous emission from a strongly driven two-level atom are presented
Theory of Pseudomodes in Quantum Optical Processes
This paper deals with non-Markovian behaviour in atomic systems coupled to a
structured reservoir of quantum EM field modes, with particular relevance to
atoms interacting with the field in high Q cavities or photonic band gap
materials. In cases such as the former, we show that the pseudo mode theory for
single quantum reservoir excitations can be obtained by applying the Fano
diagonalisation method to a system in which the atomic transitions are coupled
to a discrete set of (cavity) quasimodes, which in turn are coupled to a
continuum set of (external) quasimodes with slowly varying coupling constants
and continuum mode density. Each pseudomode can be identified with a discrete
quasimode, which gives structure to the actual reservoir of true modes via the
expressions for the equivalent atom-true mode coupling constants. The quasimode
theory enables cases of multiple excitation of the reservoir to now be treated
via Markovian master equations for the atom-discrete quasimode system.
Applications of the theory to one, two and many discrete quasimodes are made.
For a simple photonic band gap model, where the reservoir structure is
associated with the true mode density rather than the coupling constants, the
single quantum excitation case appears to be equivalent to a case with two
discrete quasimodes
Non-Markovian Decay of a Three Level Cascade Atom in a Structured Reservoir
We present a formalism that enables the study of the non-Markovian dynamics
of a three-level ladder system in a single structured reservoir. The
three-level system is strongly coupled to a bath of reservoir modes and two
quantum excitations of the reservoir are expected. We show that the dynamics
only depends on reservoir structure functions, which are products of the mode
density with the coupling constant squared. This result may enable pseudomode
theory to treat multiple excitations of a structured reservoir. The treatment
uses Laplace transforms and an elimination of variables to obtain a formal
solution. This can be evaluated numerically (with the help of a numerical
inverse Laplace transform) and an example is given. We also compare this result
with the case where the two transitions are coupled to two separate structured
reservoirs (where the example case is also analytically solvable)
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