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)