• At thermal equilibrium, F=2 and F=3 states are

equally populated (kBT>>ΔE at room temp)

• Optical pump effectively moves ground-state

population from F=3 to F=2

• Raman Pump sees depletion, Raman Probe sees gain

• Pump and Probe must be detuned because absorption

is too high on resonance

• Rb85 vapor cell is magnetically

shielded using μ-metal box

• Raman Probe is downshifted from

Raman Pump by 3.034 GHz (ground

state hyperfine splitting in Rb85) via

double-pass AOM setup

• Raman Pump and Probe are

orthogonally polarized and

copropagate through vapor –

photodetectors monitor

gain/depletion of these beams

• Optical pump propagates slightly off-

axis but still with good spatial

overlap

• AOM frequency scan centered around 3.034 GHz

• Saw up to 20% depletion of Raman pump

• FWHM ≈1 MHz for both Raman depletion dip and Raman gain peak

• Will need to use stronger Raman probe in order to more significantly deplete a more powerful Raman pump – AOM alone cannot do this

Raman Pump Depletion

Raman Probe Gain

1

2

than one. Hence, the resonant frequency shift with respect to the length variation decreases compared to the shift in an empty

cavity. For anomalous dispersion (ng<1), the frequency shift is

amplified to be equal to 1/ng times the amount of the shift in the empty

cavity.

In order to determine the actual value of R for an active cavity, we

need first to establish the explicit

dependence of on the lasing

frequency, . To this end, we first

solve Eq. (3.b) in steady state ( )

so that for . Since

is a function of E and , the

solution to the equation yields the

saturated electric field E in steady

state inside the laser cavity as a

function of the lasing frequency .

Let us consider the case in which

the cavity contains a medium with a

narrow absorption as well as a

medium with a broad gain. This configuration creates a gain profile with a dip in the center. The

imaginary part of the susceptibility can then be written as:

(5.a)

Where , (k = e or i). We use the subscript “e” for the “envelope” gain

profile and “i” for the narrower absorption profile .

Using the modified Kramers-Kronig (MKK) relation4 for the saturated susceptibility, we can

then express the real part of the susceptibility as:

(5.b)

Here i ( e) is the Rabi frequency equal to ( ) where ( ) is the dipole moment

associated with the absorbing (amplifying) medium. The gain and the absorption linewidths are

denoted by e and i, respectively. Using the Wigner–Weisskopf modelxxv

for spontaneous

emission, we can define two parameters: and . In terms of these

parameters, the Rabi frequencies can then be expressed as and . The gain

parameters can then be expressed as and , where 0 is the permittivity

Fig. 5. Energy levels for (a) 795-nm Rb laser to produce broadband gain, (b) Raman

depletion to induce narrowband absorption dip. (c) Schematics of the experimental set-

up to realize a superluminal laser: PBS, polarizing beam splitter; BS, beam splitter;

AOM, acousto-optic modulator. Note that the superluminal laser is the same as the

Raman pump. The scheme shown is for 85

Rb atoms. The broadband gain is produced by side-pumping with a diode laser array.

• Verify that Raman pump and probe are

experiencing Raman depletion and gain,

respectively

• Verify that this depletion leads to an

anomalously-dispersive laser for which

sensitivity is enhanced.

• Implement this mechanism into various

architectures to create useful and

sophisticated metrological devices

• Investigate and pursue other possible

approaches to creating a superluminal

laser (e.g. dual-peaked Raman laser)

1

2

than one. Hence, the resonant frequency shift with respect to the length variation decreases compared to the shift in an empty

cavity. For anomalous dispersion (ng<1), the frequency shift is

amplified to be equal to 1/ng times the amount of the shift in the empty

cavity.

In order to determine the actual value of R for an active cavity, we

need first to establish the explicit

dependence of on the lasing

frequency, . To this end, we first

solve Eq. (3.b) in steady state ( )

so that for . Since

is a function of E and , the

solution to the equation yields the

saturated electric field E in steady

state inside the laser cavity as a

function of the lasing frequency .

Let us consider the case in which

the cavity contains a medium with a

narrow absorption as well as a

medium with a broad gain. This configuration creates a gain profile with a dip in the center. The

imaginary part of the susceptibility can then be written as:

(5.a)

Where , (k = e or i). We use the subscript “e” for the “envelope” gain

profile and “i” for the narrower absorption profile .

Using the modified Kramers-Kronig (MKK) relation4 for the saturated susceptibility, we can

then express the real part of the susceptibility as:

(5.b)

Here i ( e) is the Rabi frequency equal to ( ) where ( ) is the dipole moment

associated with the absorbing (amplifying) medium. The gain and the absorption linewidths are

denoted by e and i, respectively. Using the Wigner–Weisskopf modelxxv

for spontaneous

emission, we can define two parameters: and . In terms of these

parameters, the Rabi frequencies can then be expressed as and . The gain

parameters can then be expressed as and , where 0 is the permittivity

Fig. 5. Energy levels for (a) 795-nm Rb laser to produce broadband gain, (b) Raman

depletion to induce narrowband absorption dip. (c) Schematics of the experimental set-

up to realize a superluminal laser: PBS, polarizing beam splitter; BS, beam splitter;

AOM, acousto-optic modulator. Note that the superluminal laser is the same as the

Raman pump. The scheme shown is for 85

Rb atoms. The broadband gain is produced by side-pumping with a diode laser array.