Measurement of Intracavity Quantum Fluctuations Using an...
Transcript of Measurement of Intracavity Quantum Fluctuations Using an...
Measurement of Intracavity QuantumFluctuations Using an Atomic Fluctuation
Bolometer
K. W. MurchK. L. Moore, S. Gupta and D. M. Stamper-Kurn
UC Berkeley
OSA/FiO 2007
K. W. Murch, K. L. Moore, S. Gupta, and D. M.Stamper-Kurn, quant-ph/0706.1005 (June 2007)
Temporal fluctuationsFree space:
Monochromatic Beam:
Coherent state in singlemode vacuum in othermodes
Temporal fluctuations due to “beating” between coherent stateand vacuum at other frequencies. White noise spectrum offluctuations.
CavityDensity of states isaccentuated atfrequencies near cavityresonance
Temporal fluctuations of an input coherent state is now colored.
Temporal fluctuationsIntracavity Temporal Fluctuations are not discernable outside thecavity
Temporal fluctuationsTo sense these fluctuations we introduce an ultracold gas into thecavity.
The atoms sense the intracavity field as an AC stark shift.
Atoms are buffeted by these fluctuations and heat up.
The experimental apparatus
Cavity Detuning (length)
Energy
Spectrum for10000 coupled atomsg = 2π x 14.4 MHz
AtomicResonance
50GHz
0
~ GHz
Δa = -30GHz(typical detuning)
34 MHz
2NgΔ
0
Dispersive Cavity QED(far from atomic resonances)
Presence of atoms basically changes the index of refraction in the cavityEach atom shifts the cavity resonance by an amount: g2/Δa
Cavity Detuning (length)
Energy
Spectrum for10000 coupled atomsg = 2π x 14.4 MHz
AtomicResonance
50GHz
0
~ GHz
Δa = -30GHz(typical detuning)
34 MHz
2NgΔ
0
Dispersive Cavity QED(far from atomic resonances)
Presence of atoms basically changes the index of refraction in the cavityEach atom shifts the cavity resonance by an amount: g2/Δa
frequencybare cavityresonance
ΔN=Ng2/Δa
shifted cavity resonance
detuned probe
Two features allow this simplifying assumption
(a) the atoms are and remain ultracold
kB T << h κ
(b) the atom cavity detuning is very large
g2/Δa << κ
Atoms are simply passive observers of the field;they only present a dispersive medium
Calculation of the heating rate
Cavity fluctuations lead to a heating rate:
Which is related to the spectrum of photon fluctuations,
The total heating rate is a sum of “free space”heating terms and the contribution from cavityfluctuations:
Single atom cooperativity
Spectrum of noise in acavity
Free Space
Away from the cavityresonance, the diffusionis the same as in free-space.
Cavity
Colored Spectrum offluctuations.
Fluctuations are“concentrated” atcavity resonance.
2.0
1.5
1.0
0.5
-30 -20 -10 0 10 20 30
Heat
ing
rate
(per
pho
ton)
Detuning from cavity resonance (MHz)
kT
Heating leads to an increase inthermal energy
An increase in energy is sensed by aloss of atoms from the finite depthtrap
The Bolometer
Each atom leaves with andamount of energy equal to thetrap depth on average
U
Cavity heating
frequencybare cavityresonance
shifted cavity resonance
detuned probe
SimultaneousMeasurements of N, and n:
Overall timescale is longcompared to evaporativetimescale ~3ms
Temperature remainsconstant: 4ms TOF images
Δa/2π = +100 GHz (N ~ 40,000)
Phot
on n
umbe
rNu
mbe
r (x
103 )
Time (ms)
Spectrum of noise in a cavity
Expected Diffusion
(no freeparameters)
Outlook
Miller Institute
Implications for cavity enhanced based measurement
Connections to micro-resonator/cooling work
New regime for Cavity QED
K. W. Murch, K. L. Moore, S. Gupta, and D. M. Stamper-Kurn, quant-ph/0706.1005 (June 2007)