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Noise-dissipation
Correlated
Dynamics of a
Double-well
Bose-Einstein
Condensate-reservoir
System
Kalai K. Rajagopal,
Gafurjan
Ibragimov,
Risman
M. Hasim
and
Idham A. Alias
INSPEM
& Department of
Mathematics,
University Putra
Malaysia, 43400
Serdang,
Selangor,
Malaysia.
Corresponding
Author:
Kalai Kumar
Rajagopal
Email:
kkrajagop@gmail.com
Doi : https://doi.org/10.47011/15.5.2
Cited by :
Jordan J. Phys.,
15 (5) (2022)
445-456
PDF
Received
on:
31/12/2020;
Accepted
on:
08/06/2021
Abstract:
In this
work, we
study
the
dissipative
dynamics
of a
double-well
Bose-Einstein
condensate
(BEC)
out-coupled
to
reservoir
at each
side of
its
trap.
The
sub-system
comprises
of a
simple
Bose-Hubbard
model,
where
the
interplay
of
atom-tunneling
current
and
inter-particle
interaction
are the
main
quantum
features.
The
contact
with two
separate
heat
baths
causes
dissipation
and
drives
the
system
into a
non-equilibrium
state.
The
system
is well
described
by the
Generalized
Quantum
Heisenberg-Langevin
equation.
We
considered
two
Markovian
dissipative
BEC
systems
based on
(i) the
mean-field
model
(MF),
where
the
internal
noise
has been
averaged
out and
(ii) the
noise-correlated
model (FDT).
Physical
quantities,
such as
population
imbalance,
coherence
and
entanglement
of the
system,
are
computed
for the
models.
The
two-mode
BEC
phases,
such as
the
quantum
tunneling
state
and the
macroscopic
quantum-trapping
state,
evolved
into
complicated
dynamics
by
controlling
the
non-linear
interaction
and
dissipation
strengths.
We found
that
many
important
quantum
features
produced
by the
noise-correlated
FDT
model
are not
captured
by the
mean-field
model.
Keywords:
Double-well
BEC,
Dissipation,
Noise,
Markovian,
Non-Markovian,
Fixed
points.
PACS:
03.75
Lm,
03.65 Yz,
03.75 Gg,
05.
References
[1] Javanainen,
J., Physical
Review Letters,
57 (25) (1986)
3164.
[2] Milburn,
G.J., Corney,
J.F., Wright,
E.M. and Walls,
D.F., Physical
Review A, 55 (6)
(1997) 4318.
[3] Smerzi,
A., Fantoni, S.,
Giovanazzi, S.
and Shenoy,
S.R., Physical
Review Letters,
79 (25) (1997)
4950.
[4] Raghavan,
S., Smerzi, A.,
Fantoni, S. and
Shenoy, S.R.,
Physical Review
A, 59 (1) (1999)
620.
[5] Albiez,
M., Gati, R.,
Froelling, J.,
Hunsmann, S.,
Cristiani, M.
and Oberthaler,
M.K., Physical
Review Letters,
95 (1) (2005)
010402.
[6] Gati, R.,
Hemmerling, B.,
Froelling, J.,
Albiez, M. and
Oberthaler,
M.K., Physical
Review Letters,
96 (13) (2006)
130404.
[7] Zibold,
T., Nicklas, E.,
Gross, C. and
Oberthaler,
M.K., Physical
Review Letters,
105 (20) (2010)
204101.
[8] Levy, S.,
Lahoud, E.,
Shomroni, I. and
Steinhauer, J.,
Nature, 449
(7162) (2007)
579.
[9]
Hofferberth, S.,
Lesanovsky, I.,
Schumm, T.,
Imambekov, A.,
Gritsev, V.,
Demler, E. and
Schmiedmayer,
J.,
Nature-Physics,
4 (6) (2008)
489.
[10]
Ruostekoski, J.
and Walls, D.F.,
Physical Review
A, 58 (1) (1998)
R50.
[11]
Khodorkovsky,
Y., Kurizki, G.
and Vardi, A.,
Physical Review
Letters, 100
(22) (2008)
220403.
[12] Boukobza,
E., Chuchem, M.,
Cohen, D. and
Vardi, A.,
Physical Review
Letters, 102
(18) (2009)
180403.
[13] Witthaut,
D., Trimborn, F.
and Wimberger,
S., Physical
Review Letters,
101 (20) (2008)
200402.
[14] Trimborn,
F., Witthaut, D.
and Wimberger,
S., Journal of
Physics B:
Atomic,
Molecular and
Optical Physics,
41 (17) (2008)
171001.
[15] Witthaut,
D., Trimborn,
F., and
Wimberger, S.,
Physical Review
A, 79 (3) (2009)
033621.
[16] Wang, W.,
Fu, L.B. and Yi,
X.X., Physical
Review A, 75 (4)
(2007) 045601.
[17] Huang,
Y., Tan, Q.S.,
Fu, L.B. and
Wang, X.,
Physical Review
A, 88 (6) (2013)
063642.
[18]
Ghasemian, E.
and Tavassoly,
M.K., Physics
Letters A, 380
(40) (2016)
3262.
[19]
Ghasemian, E.
and Tavassoly,
M.K., Laser
Physics, 27 (9)
(2017) 095202.
[20] Guarrera,
V., Wuertz, P.,
Ewerbeck, A.,
Vogler, A.,
Barontini, G.
and Ott, H.,
Physical Review
Letters, 107
(16) (2011)
160403.
[21]
Barontini, G.,
Labouvie, R.,
Stubenrauch, F.,
Vogler, A.,
Guarrera, V. and
Ott, H.,
Physical Review
Letters, 110 (3)
(2013) 035302.
[22]
Lindenberg, K.
and West, B.J.,
“The
Non-equilibrium
Statistical
Mechanics of
Open and Closed
Systems”, (VCH
New York, 1990).
[23] Scully,
M.O. and
Zubairy, M.S.,
“Quantum
Optics”,
(Cambridge
University
Press, 1997).
[24] Lazarou,
C.,
Nikolopoulos,
G.M. and
Lambropoulos,
P., Journal of
Physics B:
Atomic,
Molecular and
Optical Physics,
40 (12) (2007)
2511.
[25]
Nikolopoulos,
G.M., Lazarou,
C. and
Lambropoulos,
P., Journal of
Physics B:
Atomic,
Molecular and
Optical Physics,
41 (2) (2008)
025301.
[26]
Rajagopal, K.K.,
Physica A:
Statistical
Mechanics and
Its
Applications,
429 (5) (2015)
231.
[27]
Rajagopal, K.K.
and Muniandy,
S.V., Physica A:
Statistical
Mechanics and
Its
Applications,
434 (2015) 164.
[28] Yamamoto,
Y. and Imamoglu,
A., “Mesoscopic
Quantum Optics”,
(John Wiley &
Sons, Inc., New
York, 1999).
[29]
Rajagopal, K.K.
and Ibragimov,
G., Brazilian
Journal of
Physics, 50 (2)
(2020) 178.
[30] Weiss,
U., “Quantum
Dissipative
Systems”, 3rd
Edition, (World
Scientific,
Singapore,
2008).
[31]
Uhlenbeck, G.E.
and Ornstein,
L.S., Physical
Review, 36
(1930) 823.
[32] Sargsyan,
V.V., Adamian,
G.G., Antonenko,
N.V. and
Lacroix, D.,
Physical Review
A, 90 (2) (2014)
022123.
[33] Rajagopal,
K.K. and
Ibragimov, G.,
Brazilian
Journal of
Physics, 51
(2021) 944.
[34] Pethick,
C.J. and Smith,
H.,
“Bose-Einstein
Condensation in
Dilute Gases”,
(Cambridge
University
Press, 2008).
[35] Trimborn,
F., Witthaut, D.
and Korsch,
H.J., Physical
Review A, 79 (1)
(2009) 013608.
[36] Anglin,
J.R. and Vardi,
A., Physical
Review A, 64 (1)
(2001) 013605.
[37] Vardi,
A, Yurovsky,
V.A. and Anglin,
J.R., Physical
Review A, 64 (6)
(2001) 063611.
[38]
Tikhonenkov, I.,
Anglin, J.R. and
Vardi, A.,
Physical Review
A, 75 (1) (2007)
013613.
[39]
Constantinides,
A. and Mostoufi,
N., “Numerical
Methods for
Chemical
Engineers with
Matlab
Applications
with Cdrom”,
(Prentice Hall
PTR, 1999).
[40] Shampine,
L.F., Gladwell,
I., Shampine, L.
and Thompson,
S., “Solving
ODEs with Matlab”,
(Cambridge
University
Press, 2003).
[41] Perko,
L.,
“Differential
Equations and
Dynamical
Systems”, Volume
7, (Springer
Science &
Business Media,
2013).
[42] Barreira,
L. and Valls,
C., “Dynamical
Systems: An
Introduction”,
(Springer
Science &
Business Media,
2012).
[43] Bo, C.,
Lin, W.S. and
Xi, Y.X.,
Chinese Physics
Letters, 27 (7)
(2010) 070303.
[44] Kordas,
G., Wimberger,
S. and Witthaut,
D., Physical
Review A, 87 (4)
(2013) 043618.
[45] Hillery,
M. and Zubairy,
M.S., Physical
Review Letters,
96 (5) (2006)
050503.
[46] Hillery,
M. and Zubairy,
M.S., Physical
Review A, 74 (3)
(2006) 032333.
[47] Labouvie,
R., Santra, B.,
Heun, S.,
Wimberger, S.
and Ott, H.,
Physical Review
Letters, 115
(2015) 050601.
[48] Labouvie,
R., Santra, B.,
Heun, S.,
Wimberger, S.
and Ott, H.,
Physical Review
Letters, 116
(2016)
235302.
[49] Kosloff,
R.,
Quantum
Thermodynamics:
Entropy, 15
(2013) 2100.
[50] Hofer,
P.P.,
Perarnau-Llobet,
M., Miranda,
L.D.M., Haack,
G., Silva, R.,
Brask, J.B. and
Brunner, N., New
Journal of
Physics, 19 (12)
(2017) 123037.
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