Optical techniques for molecular manipulation
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Transcript Optical techniques for molecular manipulation
Light
and
Matter
Controlling matter with light
Tim Freegarde
School of Physics & Astronomy
University of Southampton
Mechanical effect of the photon
• electromagnetic waves carry momentum
P D B
• momentum flux (Maxwell stress tensor) defined
by
T P 0
t
emission
absorption
• photons carry momentum
hˆ
p k k
2
Mechanical effect of the photon
• electromagnetic waves carry momentum
emission
P D B
• momentum flux (Maxwell stress tensor) defined
by
T P 0
t
• photons carry momentum
hˆ
p k k
absorption
2
1
3
Optical scattering force
• each absorption results in a well-defined impulse
emission
• isotropic spontaneous emission causes no
average recoil
• average scattering force is therefore
absorption
F nk
where
n is photon absorption rate
2
1
4
Mechanical effect of the photon
• photons carry energy
• visible photon
• photons carry momentum
• visible photon
• momentum flux
• sunlight
E
4 1019 J
p k
1027 kg m.s 1
TS c
5 106 N.m 2
Cosmos 1, due for launch early 2004
© Michael Carroll, The Planetary Society
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Solar sails and comet tails
• photons carry energy
• visible photon
• photons carry momentum
• visible photon
E
4 1019 J
p k
1027 kg m.s 1
TS c
6
2
Comet Hale-Bopp, 1997
• sunlight
5
10
N
.
m
© Malcolm Ellis
• momentum flux
Cosmos 1, due for launch early 2004
© Michael Carroll, The Planetary Society
6
Acousto-optic modulation
• Fraunhofer diffraction condition
kd
crystal
a sin i sin kd
d
a
i d
d i a
ki
• Bragg diffraction condition
• Doppler shift
phonon
kd ki ka
• energy
kd
i
a
transducer
ki
and momentum k are conserved
7
Optical dipole force
• high
• force is gradient of dipole potential
towards
high intensity
• low
E
P
1
U
P.E
2
• depends upon real part of susceptibility
towards
low intensity
G=0.050
Re
P
1
0
Im
0
freq
E
8
Optical dipole force
kr
p2
2m
2
k+k
1
k atom
recoil
ki
k-k
• dipole interaction scatters photon
between initial and refracted beams
• maximum recoil
2k
momentum
k
9
Optical tweezers
Controlled rotation of small glass rod
Trapping and rotation of microscopic
silica spheres
© Kishan Dholakia, University of St Andrews
10
Diffracting atoms
40
Ar
32 rad
v 850 m.s -1
Ar 0.012 nm
1.25 m
811 nm
E M Rasel et al, Phys Rev Lett 75 2633 (1995)
11
Optical scattering force
• electromagnetic waves carry momentum
k
emission
• photon absorption gives a well-defined impulse
• isotropic spontaneous emission causes no
average recoil
absorption
• average scattering force is therefore
F nk
where
n
is photon absorption rate
• maximum absorption rate is
nmax 1 2
2
1
12
Optical forces
• electromagnetic waves carry momentum
F x
k
V x
emission
• forces therefore accompany radiative interactions
• position-dependent interaction
gives position-dependent force
TRAPPING
absorption
x
dV
F
1 dx
2
13
Optical forces
• electromagnetic waves carry momentum
k
F vx
V vx
• forces therefore accompany radiative interactions
• position-dependent interaction
gives position-dependent force
TRAPPING
• velocity-dependent interaction
gives velocity-dependent force
COOLING
vx
dV
F
dvx
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Optical forces
POSITION
continuous
wave
magneto-optic
dipole
modulated
c.w.
pulsed
VELOCITY
Sisyphus
dynamical (cavity)
Doppler
VSCPT
stochastic
adiabatic
time-of-arrival
TRAPPING
Raman
interferometric
COOLING
15
Doppler cooling
p2
2m
• use the Doppler effect to provide a velocitydependent absorption
2
• photon absorption gives a well-defined impulse
• red-detuned photon reduces momentum
1
• spontaneous emission gives no average impulse
momentum
k
16
Doppler cooling
p2
2m
• use the Doppler effect to provide a velocitydependent absorption
2
• photon absorption gives a well-defined impulse
• red-detuned photon reduces momentum
1
• spontaneous emission gives no average impulse
• illuminate from both (all) directions
• sweep wavelength to cool whole distribution
momentum
k
17
Zeeman slowing
• opposite circular polarizations see
opposite shifts in transition frequency in
presence of longitudinal magnetic field
ZEEMAN
EFFECT
mJ 1
2
mJ 0
• Zeeman / Faraday effect
mJ 1
atomic
beam
B
tapered
solenoids
red-detuned
(-) laser beam
mJ 0
1
0
B
18
Optical ion speed limiter
accelerating
ions
red-detuned
laser beam
• electrostatic acceleration cancelled by radiation pressure deceleration
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Magneto-optical trap
LCP
mJ 1
mJ 0
RCP
RCP
mJ 1
RCP
RCP
anti-Helmholtz
coils
LCP
RCP
RCP
mJ 0
0
B
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Magneto-optical trap
LCP
• Zeeman tuning in inhomogeneous magnetic
field provides position-dependent absorption
• red-detuned laser beams also produce
Doppler cooling
RCP
RCP
RCP
RCP
anti-Helmholtz
coils
• sweep frequency towards resonance for
coldest trapped sample
• typical values: 107 atoms, 10μK
LCP
21
Quantum description of atomic polarization
• spatial part of eigenfunctions given by 1 and 2
energy
• full time-dependent eigenfunctions therefore
2 r, t 2 exp i0t
0
1 r, t 1
• any state of the two-level atom may hence be written
r, t a 1 b 2 exp i0t
0
2
1
22
Quantum description of atomic polarization
• spatial part of eigenfunctions given by 1 and 2
• full time-dependent eigenfunctions therefore
2 r, t 2 exp i0t
1 r, t 1
write time-dependent
Schrödinger equation for
two-level atom
insert energy of interaction
with oscillating electric field
• any state of the two-level atom may hence be written
r, t a 1 b 2 exp i0t
reduce to coupled equations
for a(t) and b(t)
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Quantum description of atomic polarization
eigenfunctions
given
• spatial part of
by 1 and 2
2
i
V
• full time-dependent
eigenfunctions
therefore
t
2m
2
2 r, t 2 exp i0t
V r, t e x E0 cos t
r, t 1
1
write time-dependent
Schrödinger equation for
two-level atom
insert energy of interaction
with oscillating electric field
• any state of the two-level atom may hence be written
r, t a 1 b 2 exp i0t
reduce to coupled equations
for a(t) and b(t)
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Rabi oscillations
• solve for initial condition that, at t 0,
aa 1, bb 0
• solutions are
a cos 2 t
2
2
b sin 2 t
where
write time-dependent
Schrödinger equation for
two-level atom
e E0
2
1x2
is the Rabi frequency
insert energy of interaction
with oscillating electric field
reduce to coupled equations
for a(t) and b(t)
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Rabi oscillations
• solve for initial condition that, at t 0,
b
aa 1, bb 0
• solutions are
a cos 2 t
2
a
2
b sin 2 t
where
e E0
2
1x2
a
is the Rabi frequency
b
2
2
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Pi-pulses
• coherent emission as well as
absorption
• half-cycle of Rabi oscillation
provides complete population
transfer between two states
2
RABI OSCILLATION
1
time
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Coherent deflection
• two photon impulses
p
• atom returned to initial state
• b experiences opposite impulse
b, p k
a, p
a, p 2k
p
Kazantsev, Sov Phys JETP 39 784 (1974)
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Amplification of cooling
p
b, p k
a, p
pz
t
velocity
selective
excitation
p
p
spontaneous
emission
a
b
a
b
a
b
a
b
a
b
p
p
b, p n 1k
a, p n2k
a, p nk
a, p nk
p
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Stimulated scattering: focussing and trapping
München
30
Stimulated scattering: focussing and trapping
München
Garching
plane of
coincidence
• first bus is more likely to be heading towards plane of coincidence
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Stimulated scattering: focussing and trapping
k
plane of
coincidence
k
• first pulse excites ………………….
photon absorbed
• second pulse stimulates decay…
photon emitted
• coherent process – can be repeated many times
• spontaneous emission only in overlap region
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Stimulated scattering: focussing and trapping
p
p
p
rectangular
Sech2
Gaussian
FORCE
rectangular
Sech2
Gaussian
plane of coincidence
p
HEATING
p
p
Freegarde et al, Opt Commun 117 262 (1995)
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Stimulated scattering: focussing and trapping
EXPERIMENTAL DEMONSTRATION
• 852 nm transition in Cs
• 30 ps, 80 MHz sech2 pulses from Tsunami
• stimulated force ~10x max spontaneous force
rectangular
Sech2
Gaussian
FORCE
HEATING
rectangular
Sech2
Gaussian
Freegarde et al, Opt Commun 117 262 (1995)
Goepfert et al, Phys Rev A 56 R3354 (1997)
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Atom interferometry
p/2 pulses
2
RABI OSCILLATION
• quarter Rabi cycles
• atomic beam-splitters
i
1
e
2
• pure states become
2
1
time
35
Stimulated scattering: interferometry
• excitation probability depends on ψ
• ‘spin echo’, Ramsey spectroscopy
2
ψ
1
p/2
p/2
36
Stimulated scattering: interferometric cooling
p
• coherent sequence of operations on
atomic/molecular sample
b, p k
• short pulses spectral insensitivity
M Weitz, T W Hänsch, Europhys Lett 49 302 (2000)
a, p
a, p 2k
• pulses form mirrors of atom/molecule
interferometer
• velocity-dependent phase:
p/2 impulses add or cancel
p
b, p k
a, p
a, p
b, p k
p/2
p/2
z
t
37
Stimulated scattering: interferometric cooling
VELOCITY-DEPENDENT PHASE
• variation of phase with kinetic energy:
e iEt where E p 2 2m, p nk
n 1 ψ k m p t nr t
b
a
ψ
• hence velocity-dependent impulse
and cooling…
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Light and Matter
• next :
Monday 5 Jan: Q & A
Thursday 9 Jan: problem sheet 3
• for handouts, links and other material, see
http://www.phys.soton.ac.uk/quantum/phys3003.htm
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