Quantum Speed-Up of Field Evolution by Atomic Number
in an Optical Cavity QED System.
Burkley D. Patterson1, Andres D. Cimmarusti1&, Luke P. Corcos1 Zhihui Yan1 2, Sebastian Deffner3#, Luis A. Orozco1,.
1Joint
Quantum Institute, University of Maryland and NIST, College Park, MD 20742, USA. 2State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi
University, Taiyuan 030006, People's Republic of China.. 3#Department of Chemistry and Biochemistry , Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742, USA.
Work supported by the National Science Foundation of the United States.& Currently at Intel, Portland, OR, USA. # Currently at the Theory Division, Los Alamos National Laboratory, Los Alamos, NM, USA.
Motivation
Manipulation of the evolution rate of an open quantum system by
tailoring the environment is desirable in areas from quantum
information to optimal quantum control and feedback. In Cavity
QED, by considering the system as only the field, and the atoms a
part of the reservoir, it is possible to tailor the “environment” in such
a way as to speed up the refilling of the cavity once a photon has
escaped [1] .
Figure 3. Non-Markovianity of a Cavity QED system, as a function of
atom number [4]
Theory
Our apparatus consists of an optical cavity with escape rate κ, weakly
driven by the electric field ε, to produce a field that dipole-couples with
rate gN1/2 to N two-level atoms (decay rate γ). We focus on the escaping
field of the system as we change the coupling gN1/2. (See Fig. 1).
Figure 1. Two pictures of the Cavity QED system.
The system (cavity field) has a non-Markovian character (Fig 3.
shows a calculation of this quantity) as the excitation that goes to the
atoms can come back to the cavity and the speed will depend on the
number of atom that we have.
Experimental Results
A correlation for a particular number of atoms is in Fig 4. The
continuous line is a fit to an inverted Lorentzian to extract the height
of the peak and the half width at half maximum (hwhm). The excess
noise visible in the steady state (τ=200 ns) comes from the atomic
transit time.
Cavity QED shows antibunching and sub-Poissonian behavior. Here,
our focus is on the speed, as measured by the point of maximum slope
on the recovery to steady state. The normalized correlation function for
the intensity, which gives the conditional intensity after the detection of
a photon, is [2]:
Figure 6. a) Measured rate of evolution as a function of coupling to
the N atoms showing an increase (the dashed line is to guide the
eye) b) Simulation of the rate of evolution that includes random
position of a distribution of atom in the mode of the cavity.
2






∆α
(κ + γ /2)τ
(κ + γ /2)
(2)
exp  −
× coshΩτ +
sinhΩτ  
g (τ ) = 1+


 

2
α
2Ω

Summary
with :


 ε  1  ∆α
2C
C1
α =  
= −2C1 ' 
, and Ω =
,
, C1 ' =
 κ  1+ 2C  α
(1+ γ /2κ )
 (1+ 2C − 2C1 ' 
1
κ − γ /2) − g 2 N
(
4
Figure 4. g(2)(τ) with sub-Poissonian and antibunching character.
Calculated correlation functions, are shown in Figure 2
We have measured the increase in the quantum speed of the
field of a Cavity-QED system as the number of atoms changes.
We plan to implement feedback such that dynamic changes in
the number of atoms can help control the conditional state of the
system.
References and Acknowledgments
Figure 2. Calculated correlation function for different numbers of atoms
(N), with a random distribution of atoms and g depending on the position
of the atoms in the cavity mode.
Red N=1, green N=10, blue N=100. The dashed green line is without
averaging for N=10.
Figure 5. Measured rate of evolution as a function of coupling to the N
atoms for a system with bunching character
The change of the steady state recovery rate in the Cavity QED
system appears linear with vacuum Rabi splitting Ω which depends
on N1/2 in Fig. 6 where both data (a) and simulation (b) show the
increase.
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2 H. J. Carmichael, R. J. Brecha, and P. R. Rice, Opt. Commun. 82,
73 (1991).
3 A. D. Cimmarusti, C. A. Schroeder, B. D. Patterson, L. A. Orozco,
P. Barberis-Blostein, and H. J. Carmichael, New J. Phys. 15, 013017
(2013).
4 H-P Breuer, E-M Laine and J Piilo, Phys. Rev. Lett. 103, 210401
(2009)
We would like to acknowledge the help of Howard Carmichael.