20 research outputs found
Atom state evolution and collapse in ultracold gases during light scattering into a cavity
We consider the light scattering from ultracold atoms trapped in an optical
lattice inside a cavity. In such a system, both the light and atomic motion
should be treated in a fully quantum mechanical way. The unitary evolution of
the light-matter quantum state is shown to demonstrate the non-trivial phase
dependence, quadratic in the atom number. This is essentially due to the
dynamical self-consistent nature of the light modes assumed in our model. The
collapse of the quantum state during the photocounting process is analyzed as
well. It corresponds to the measurement-induced atom number squeezing. We show
that, at the final stage of the state collapse, the shrinking of the width of
the atom number distribution behaves exponentially in time. This is much faster
than the square root time dependence, obtained for the initial stage of the
state collapse. The exponentially fast squeezing appears due to the discrete
nature of the atom number distribution.Comment: 10 pages, 1 figur
Cavity enhanced light scattering in optical lattices to probe atomic quantum statistics
Different quantum states of atoms in optical lattices can be nondestructively
monitored by off-resonant collective light scattering into a cavity. Angle
resolved measurements of photon number and variance give information about
atom-number fluctuations and pair correlations without single-site access.
Observation at angles of diffraction minima provides information on quantum
fluctuations insensitive to classical noise. For transverse probing, no photon
is scattered into a cavity from a Mott insulator phase, while the photon number
is proportional to the atom number for a superfluid.Comment: 4 pages, 3 figures, to published in Phys. Rev. Lett. (March 2007
Light scattering from ultracold atoms in optical lattices as an optical probe of quantum statistics
We study off-resonant collective light scattering from ultracold atoms
trapped in an optical lattice. Scattering from different atomic quantum states
creates different quantum states of the scattered light, which can be
distinguished by measurements of the spatial intensity distribution, quadrature
variances, photon statistics, or spectral measurements. In particular,
angle-resolved intensity measurements reflect global statistics of atoms (total
number of radiating atoms) as well as local statistical quantities (single-site
statistics even without an optical access to a single site) and pair
correlations between different sites. As a striking example we consider
scattering from transversally illuminated atoms into an optical cavity mode.
For the Mott insulator state, similar to classical diffraction, the number of
photons scattered into a cavity is zero due to destructive interference, while
for the superfluid state it is nonzero and proportional to the number of atoms.
Moreover, we demonstrate that light scattering into a standing-wave cavity has
a nontrivial angle dependence, including the appearance of narrow features at
angles, where classical diffraction predicts zero. The measurement procedure
corresponds to the quantum non-demolition (QND) measurement of various atomic
variables by observing light.Comment: 15 pages, 5 figure
Bond Order via Light-Induced Synthetic Many-body Interactions of Ultracold Atoms in Optical Lattices
We show how bond order emerges due to light mediated synthetic interactions
in ultracold atoms in optical lattices in an optical cavity. This is a
consequence of the competition between both short- and long-range interactions
designed by choosing the optical geometry. Light induces effective many-body
interactions that modify the landscape of quantum phases supported by the
typical Bose-Hubbard model. Using exact diagonalization of small system sizes
in one dimension, we present the many-body quantum phases the system can
support via the interplay between the density and bond (or matter-wave
coherence) interactions. We find numerical evidence to support that dimer
phases due to bond order are analogous to valence bond states. Different
possibilities of light-induced atomic interactions are considered that go
beyond the typical atomic system with dipolar and other intrinsic interactions.
This will broaden the Hamiltonian toolbox available for quantum simulation of
condensed matter physics via atomic systems.Comment: Accepted in New Journal of Physic
Non-Hermitian Dynamics in the Quantum Zeno Limit
Measurement is one of the most counter-intuitive aspects of quantum physics.
Frequent measurements of a quantum system lead to quantum Zeno dynamics where
time evolution becomes confined to a subspace defined by the projections.
However, weak measurement performed at a finite rate is also capable of locking
the system into such a Zeno subspace in an unconventional way: by Raman-like
transitions via virtual intermediate states outside this subspace, which are
not forbidden. Here, we extend this concept into the realm of non-Hermitian
dynamics by showing that the stochastic competition between measurement and a
system's own dynamics can be described by a non-Hermitian Hamiltonian. We
obtain an analytic solution for ultracold bosons in a lattice and show that a
dark state of the tunnelling operator is a steady state in which the
observable's fluctuations are zero and tunnelling is suppressed by destructive
matter-wave interference. This opens a new venue of investigation beyond the
canonical quantum Zeno dynamics and leads to a new paradigm of competition
between global measurement backaction and short-range atomic dynamics.Comment: Accepted in Phys. Rev.
Incoherent quantum feedback control of collective light scattering by Bose-Einstein condensates
It is well known that in the presence of a ring cavity the light scattering
from a uniform atomic ensemble can become unstable resulting in the collective
atomic recoil lasing. This is the result of a positive feedback due to the
cavity. We propose to add an additional electronic feedback loop based on the
photodetection of the scattered light. The advantage is a great flexibility in
choosing the feedback algorithm, since manipulations with electric signals are
very well developed. In this paper we address the application of such a
feedback to atoms in the Bose-Einstein condensed state and explore the quantum
noise due to the incoherent feedback action. We show that although the feedback
based on the photodetection does not change the local stability of the initial
uniform distribution with respect to small disturbances, it reduces the region
of attraction of the uniform equilibrium. The feedback-induced nonlinearity
enables quantum fluctuations to bring the system out of the stability region
and cause an exponential growth even if the uniform state is globally stable
without the feedback. Using numerical solution of the feedback master equation
we show that there is no feedback-induced noise in the quadratures of the
excited atomic and light modes. The feedback loop, however, introduces
additional noise into the number of quanta of these modes. Importantly, the
feedback opens an opportunity to position the modulated BEC inside a cavity as
well as tune the phase of scattered light. This can find applications in
precision measurements and quantum simulations.Comment: 7 pages, 7 figure
Multipartite Entangled Spatial Modes of Ultracold Atoms Generated and Controlled by Quantum Measurement
We show that the effect of measurement back-action results in the generation
of multiple many-body spatial modes of ultracold atoms trapped in an optical
lattice, when scattered light is detected. The multipartite mode entanglement
properties and their nontrivial spatial overlap can be varied by tuning the
optical geometry in a single setup. This can be used to engineer quantum states
and dynamics of matter fields. We provide examples of multimode generalizations
of parametric down-conversion, Dicke, and other states, investigate the
entanglement properties of such states, and show how they can be transformed
into a class of generalized squeezed states. Further, we propose how these
modes can be used to detect and measure entanglement in quantum gases.Comment: 6 Pages, 3 Figures, Supplemental Material include