30,254 research outputs found
Dynamics of many-body photon bound states in chiral waveguide QED
We theoretically study the few- and many-body dynamics of photons in chiral
waveguides. In particular, we examine pulse propagation through a system of
two-level systems chirally coupled to a waveguide. We show that the system
supports correlated multi-photon bound states, which have a well-defined photon
number and propagate through the system with a group delay scaling as
. This has the interesting consequence that, during propagation, an
incident coherent state pulse breaks up into different bound state components
that can become spatially separated at the output in a sufficiently long
system. For sufficiently many photons and sufficiently short systems, we show
that linear combinations of -body bound states recover the well-known
phenomenon of mean-field solitons in self-induced transparency. For longer
systems, however, the solitons break apart through quantum correlated dynamics.
Our work thus covers the entire spectrum from few-photon quantum propagation,
to genuine quantum many-body (atom and photon) phenomena, and ultimately the
quantum-to-classical transition. Finally, we demonstrate that the bound states
can undergo elastic scattering with additional photons. Together, our results
demonstrate that photon bound states are truly distinct physical objects
emerging from the most elementary light-matter interaction between photons and
two-level emitters. Our work opens the door to studying quantum many-body
physics and soliton physics with photons in chiral waveguide QED.Comment: Updated with new results. 14 pages plus supplementary materia
Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
We propose new compressive parameter estimation algorithms that make use of
polar interpolation to improve the estimator precision. Our work extends
previous approaches involving polar interpolation for compressive parameter
estimation in two aspects: (i) we extend the formulation from real non-negative
amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch
between the manifold described by the parameters and its polar approximation.
To quantify the improvements afforded by the proposed extensions, we evaluate
six algorithms for estimation of parameters in sparse translation-invariant
signals, exemplified with the time delay estimation problem. The evaluation is
based on three performance metrics: estimator precision, sampling rate and
computational complexity. We use compressive sensing with all the algorithms to
lower the necessary sampling rate and show that it is still possible to attain
good estimation precision and keep the computational complexity low. Our
numerical experiments show that the proposed algorithms outperform existing
approaches that either leverage polynomial interpolation or are based on a
conversion to a frequency-estimation problem followed by a super-resolution
algorithm. The algorithms studied here provide various tradeoffs between
computational complexity, estimation precision, and necessary sampling rate.
The work shows that compressive sensing for the class of sparse
translation-invariant signals allows for a decrease in sampling rate and that
the use of polar interpolation increases the estimation precision.Comment: 13 pages, 5 figures, to appear in IEEE Transactions on Signal
Processing; minor edits and correction
Fully quantum mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator
We analyze the dynamics of single photon transport in a single-mode waveguide
coupled to a micro-optical resonator using a fully quantum mechanical model. We
examine the propagation of a single-photon Gaussian packet through the system
under various coupling conditions. We review the theory of single photon
transport phenomena as applied to the system and we develop a discussion on the
numerical technique we used to solve for dynamical behavior of the quantized
field. To demonstrate our method and to establish robust single photon results,
we study the process of adiabatically lowering or raising the energy of a
single photon trapped in an optical resonator under active tuning of the
resonator. We show that our fully quantum mechanical approach reproduces the
semi-classical result in the appropriate limit and that the adiabatic invariant
has the same form in each case. Finally, we explore the trapping of a single
photon in a system of dynamically tuned, coupled optical cavities.Comment: 24 pages, 10 figure
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