Download Mechanical momentum transfer to magneto

KFKI RESEARCH INSTITUTE
FOR PARTICLE AND NUCLEAR PHYSICS
OF THE HUNGARIAN ACADEMY OF SCIENCES
Mechanical momentum transfer to magnetooptically trapped atoms by frequency
modulated laser pulses
J.S. Bakos, G. Demeter, G.P. Djotyan, P.N. Ignácz,
M.Á. Kedves, B. Ráczkevi, Zs. Sörlei, J. Szigeti, D. Dzsotján
Mechanical momentum transfer
Optical manipulation:
absorption →
ƒ
spontaneous decay
ƒ
stimulated emission
Coherent manipulation without heating
π pulses or ARP
→ atom optics
(interferometry, lithography)
Other schemes:
STIRAP, Bichromatic standing wave,
Frequency modulated standing wave,
Frequency-chirped optical lattice ... etc
Coherent population transfer in Rb atoms by
frequency-chirped laser pulses
Computer code for the Bloch
Equations for density matrix
elements takes into account:
the effect of the frequency
modulated light pulses,
the spontaneous decay of the
excited states,
the effect of the hyperfine
pumping.
It describes the temporal behavior
of the populations, and shows
possibility for effective population
transfer between the ground and
excited states.
Phys.Rev A 68,
68, 053409,2003, G.P. Djotyan,
Djotyan, J.S. Bakos,
G. Demeter, P.N. Ignácz,
,
M.Á.
Kedves,
Zs.
Ignácz
Zs. Sörlei,
Sörlei,
J.Szigeti,
J.Szigeti, Z.L. Tóth, Coherent population transfer in Rb
atoms by frequencyfrequency-chirped laser pulses
Population dynamics for two consecutive pulses
broadband pumping
(ground states not resolved)
narrow band pumping
(ground states resolved)
Effective transfer may be achieved!
Experimental arrangement
Experimental arrangement
Generation of chirped pulses
F-P FSR 20GHz, F=40
Measurement of the chirp
with
Spectrograph and F-P
with
Fast photodiode
Pulse train
Displacement of the trapped atoms
spontaneous force
induced force
Displacement of the atoms
Displacement of the atomic cloud after the interaction with
~ 5000 chirped pulses or pulse pairs
a ≈ 105 m/s2
Population of the excited states
The model discussed in the
theoretical work was
developed to the real
experimental conditions,
taking into account the time
and frequency dependence
of the laser pulses
depending on the offset of
the dc current of the laser
diode.
N = sum of the populations of the
excited levels
Two other cases:
Momentum transferred to the atoms by partially
overlapping chirped pulses: two-level model
Schrödinger equation was studied
numerically for various pulse
parameters, without taking into
account spontaneous emission.
Gaussian pulses with linear chirp were
considered, whose central frequency
were resonant with the atomic
transition.
From the final wave function
extracted:
G. Demeter, G. P. Djotyan,
Djotyan, Zs. Sörlei,
Sörlei, and
J. S. Bakos,
Bakos, Mechanical effect of
retroreflected frequencyfrequency-chirped laser
pulses on twotwo-level atoms.
atoms.
Phys. Rev. A 74, 013401 (2006)
average momentum transferred to the
atoms after the interaction with a
single pulse pair,
spreading of the wave function in
momentum space
final population of the levels.
Final momentum expectation value and
momentum spread (heating) after the action of a
pulse pair depending on the delay
Initial condition: atoms in the ground state,
infinitely sharp momentum distribution
Final momentum distribution after
the action of two pulses
Even multiples ħk ~> plateaous, ground state,
between plateaous transitions are possible to 4 final states.
Odd multiples ħk ~> excited state, +/- ħk.
→ beam splitter
Repeated interaction:Effect of several cycles on the
momentum distribution, taking into account the
spontaneous emission
Overlapping pulses: the atoms spend less time in excited state,
fewer cycles are necessary to get the same
momentum transfer
Model adapted to the experimental
conditions
A computer simulation was performed along similar lines of the theoretical
model. Two-level atoms were considered interacting with two,
counterpropagating laser pulses.
To include the effects of spontaneous emission, the master equation for the
density matrix in monentum space was simulated. This was achieved by
using the momentum-space Schrödinger equation for a two-level atom
augmented with phenomenological decay terms and solved using the
Monte-Carlo Wave Function.
The decay constant was taken to be 1/27ns. To obtain pulse shapes and
chirp rates that match those of the experiment, the Rabi frequencies and the
time-dependent phases of the pulses needed in the equations were
calculated by considering the intensity and frequency modulated laser beam
passing through the Fabry-Perot interferometer. Thus the simulation took
full account of the pulse widening in regions where chirp is slower and also
the emergence of smaller pulses.
Final momentum distribution and momentum spread
depending on the diode laser central frequency offset.
The experimentally generated pulse shapes and chirps are
simulated
momentum
spreading
Momentum transferred by the overlapping pulses
depending on the laser intensity
Timing of the measurement with overlapping pulses,
trap beams were switched off during the interaction
Experimental conditions were
the same as earlier, but the
trapping laser was disclosed
for the time of the measurement.
(No trap force)
The beam diameter was smaller,
than at the earlier measurement.
(Larger intensity)
When the dc offset of the laser
was large from the resonance of
the Rb line, the pulses were much
longer than the delay,
(slow chirp) (Robust overlapping)
Displacement of the atomic cloud after the interaction with
a pulse train of ~5000 pulses or pulse pairs
Measurement of the spreading of the atom packet
after the interaction with a pulse train of ~5000 pulses or
pulse pairs
Preparation of chirped laser pulses in the ns range
by using electro-optical modulators
A more direct way to produce frequency chirped light pulses is using electro-optical
phase (PM) and amplitude (AM) modulators.
Fiber coupled, low rf power controlled integrated - optics modulators are available in the
NIR.
Recently published examples:
Rogers CE, Wright MJ, Carini JL, Pechkis JA, Gould PL, Generation of arbitrary frequency chirps
with a fiberfiber-based phase modulator and selfself-injectioninjection-locked diode laser.
JOSA B, 24, 1249, 2007
•
X. Miao, E. Wertz, M. G. Cohen, and H. Metcalf, Strong optical
optical forces from adiabatic rapid passage
PRA 75, 011402_R (2007)
•
Integrated-optic AMs are constructed by patterning Mach-Zender interferometer on an
electro optic substrate, and phase induced in each optical pathes of the modulator
Chirp parameter: ratio between the phase and intensity modulation.
z-cut AM:
chirp parameter ≠ 0
Our preliminary investigations:
it is possible to generate chirped light pulses with a single AM.
Desired parameters of the pulses can be achived by the waveform and amplitude of the
RF signal, and DC bias level.
Desired: linear chirp →
quadratic phase change
If we apply the "scalp" of a sinusoidal signal for the AM, we can get a linear chirp.
Drawback: low light power is allowed.
Mach-Zender z-cut AM modulators
α 0 = 0.70 ± 0.05
Measurement of the intrinsic chirp parameter of the
modulator EOSPACE-Model AZ-0K5-10-PFU-PFU-780
Sinusoidal electric modulation
applied, ~> sinusoidal phase
modulation in each paths of
the M-Z interferometer.
Spectral decomposition of the
signal with a F-P
interferometer.
From the ratio of the different
order harmonic intensities the
chirp parameter can be
determind.
T. Kawanishi, K. Kogo, S. Oikawa, M.
Izutsu, Opt. Com. 195, 399, 2001.
Measurement of the chirp parameter by
interferometry
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