Download 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  nk
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 1019 J
p  k
 1027 kg m.s 1
TS c
 5 106 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 1019 J
p  k
 1027 kg m.s 1
TS 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
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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
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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
2k

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)
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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  nk
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
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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
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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
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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
19
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
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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  i0t
0
 1 r, t   1
• any state of the two-level atom may hence be written
 r, t   a 1  b 2 exp  i0t
0
2
1
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Quantum description of atomic polarization
• spatial part of eigenfunctions given by 1 and 2
• full time-dependent eigenfunctions therefore
 2 r, t   2 exp  i0t
 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  i0t
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
 eigenfunctions

 therefore
V
• full time-dependent
t
2m
2


 2 r, t   2 exp  i0t
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  i0t
reduce to coupled equations
for a(t) and b(t)
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Rabi oscillations
• solve for initial condition that, at t  0,
aa  1, bb  0
• solutions are
a  cos 2 t
2
b  sin 2 t
2
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
aa  1, bb  0
• solutions are
a  cos 2 t
2
a
b  sin 2 t
2
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  2k
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  1k
a, p  n2k
a, p  nk
a, p  nk
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)
33
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)
34
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  2k
• 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  nk
n  1 ψ  k m p t  nr 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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