Observation of polarization instabilities
in a two-photon laser
Bz
z
y
x
M.D. Stenner, W.J. Brown, O. Pfister, and
D.J. Gauthier
Duke University Department of Physics
Supported by the National Science Foundation
Two-Photon Laser
Based on two-photon stimulated emission
Ee
ωa
Ei
ωb
Eg
ωa
ωb
Proposed by Prokhorov, Sorokin, and Braslau in
1963 and 1964
Two-photon maser built by Brune et al. in 1987
Two-photon laser built by Gauthier et al. in 1992
Two-photon laser has many interesting properties
and differs from one-photon laser in many ways.
Here, I focus on nonlinear behavior.
2
Ingredients of a Laser
one-photon lasers
(Schawlow and Townes 1958)
Atoms
Pump
Mechanism
Mirror
two-photon lasers
(Sorokin and Braslau 1964)
GAIN + FEEDBACK ⇒ OSCILLATION
Review One-Photon Lasers
The Atoms
Na
Nb
h ωba
a
Concentrate on two levels
of the atom
b
3
The Light-Matter Interactions:
One-Photon Processes
Spontaneous Emission
Ee
dNe = −AN
e
dt
ωeg
A ∼ 108s−1
Eg
Absorption
Ee
dNg
I N
=
−σ
dt
h̄ωeg g
ωeg
σ ∼ 10−9cm2
Eg
Stimulated Emission
Ee
ωeg
ωeg
ωeg
dNe = −σ I N
dt
h̄ωeg e
Eg
Photons have same direction, frequency and phase
4
Two-Photon Processes
(Goeppert-Meyer, 1931)
Spontaneous Emission
Ee
same
parity E i
ωa
ωa + ωb = ωeg
ωb
Eg
dominant decay mechanism for many metastable transitions
(Briet & Teller, 1940)
Stimulated Emission
Ee
ωa
Ei
ωb
Eg
ωa = ωb =
ωeg
2
ωa
ωb
dNe
= −σ
dt
µ
¶
I 2
Ne
h̄ωa
transient two-photon gain
(Loy 1978, Schlemmer et al. 1980, Nikolaus et al. 1981)
5
Two-Photon Amplifier
Ee
Iout
Iin
Ei
ω = 1 ωeg
2
Eg
2
dI
I
= G(2)
dz
1 + I2
Solutions:
(2) I 2
for low intensity: dI
dz ≈ G
for low gain (small G(2)): Iout ∼ Iin(1+G(2)IinL)
Iout ∼ Iin
Iin −→ 0
Iout
Iin
(2) I L
G
in
e
gain −→ 0
1
0
(2)
Isat
I in
6
Nonlinearity in one-photon lasers
Laser Intensity
nonlinearity
important
laser
threshold
0
1
2
3
4
Pump Rate R/Rth
5
P (ω) = χ(ω)E(ω)
χ(ω) ∝ ∆N ∝
1
(1)
1 + I/Isat
≈1−
I
(1)
Isat
+ ···
(1)
(valid when I ¿ Isat )
P (ω) ≈ χ(1)(ω)E(ω) + χ(3)(ω)E 3(ω)
For most lasers, nonlinear behavior can be accurately described by the first two terms
7
Laser Intensity I/
(2)
Isat
Nonlinearity in two-photon lasers
4
nonlinearity
3 important
2
1
0
0
1
0.5
1.5
Pump Rate R/Rth
1

I
2
2
χ(ω) ∝ ∆N ∝
µ
¶2 6≈ 1 −  (2)  + · · ·
(2)
Isat
1 + I/Isat
(2)
The expansion does not converge because I ≥ Isat
for all operating conditions!
This system is highly nonlinear under all operating
conditions!
8
Experimental Setup
Bz
z
detector
y
mirrors
x
39
K
atoms
Raman pump
starting
pulse
optical pumps
F ≈ 15, 000
atomic number density ≈ 2 × 1010 cm−3
atoms in cavity ≈ 106
9
Two-Photon Gain via Multi-Photon
Scattering
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z
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x
25 MHz
F=2
4 2P1
F=1
ωd
homogenous width = 5 MHz
residual doppler = 30 MHz
ωp
2
ωd
ωp
F=2
4 2S1
∆ g = 462 MHz
F=1
m = -2
m = -1
m=0
Resonance condition:
m=1
m=2
∆g
ω d − ωp =
2
10
2
Threshold Behavior of the
Two-Photon Laser
Laser stable with no photons in the cavity until
perturbed by injected pulse
Laser is stable at ≈ 3 µW
11
Observation of Polarization Instabilities
We now place a linear polarizer after the laser
added linear polarizer
Total intensity is constant, but intensity in a single polarization oscillates at f = 9.1 MHz. The
intensity is stable, but the polarization is unstable.
Both periodic and random-like oscillations occur
for different magnetic field strengths.
12
Magnetic Field Dependence
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How can we have polarization
instabilities?
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z
y
x
We have seen that the
two-photon laser is highly
nonlinear, so we might
expect intensity
instabilities, but why
would we have polarization
instabilities?
• Multiple final states
• Multiple quantum pathways
• Each pathway produces a different polarization
• All pathways are frequency degenerate
14
Other pathways
ẑẑ
shown
previously
σ̂ −σ̂ +
same final
state
σ̂ +ẑ
different final
state
15
What determines the polarization
instability oscillation frequency?
We observe oscillation at f = 9.1 MHz
Other relevant frequencies in the experiment:
Raman pump detunings ≈ 25 MHz and 256 MHz
Natural linewidth ≈ 5 MHz
Doppler linewidth ≈ 30 MHz
Cavity linewidth ≈ 1 MHz
Gain-Cavity detuning unknown (nominally 0)
Oscillation frequency is comparable to both cavity
linewidth and 39K natural linewidth.
We are exploring the gain both experimentally and
theoretically to investigate further.
16
Conclusions
The two photon laser is a new quantum oscillator
with many features that demand investigation.
• Highly nonlinear behavior
• Complex polarization instabilities
• Multiple degenerate quantum pathways starting from same initial state
• Possible bright entangled state source
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