# Presentation: 470705

## Trapped Atoms in Cavity QED for Quantum Optics and Quantum Information

**Jason McKeever**
** ****Quantum Optics Group, Caltech**
**QUEST Summer Workshop**
**August 9, 2004**

**Sponsors:**Caltech MURI for Quantum Networks (ARO)
- NSFARDA
- ONR

## Outline

- Introduction and motivation: Why trap an atom in a cavity?
- State-insensitive cooling and trapping of a single atom in an optical cavity
- Cavity QED “By The Numbers” (*briefly*)
- A One-Atom Laser in the Regime of Strong Coupling
- Deterministic Generation of Single Photons
- Summary and Outlook

## Strong Coupling in Cavity QED

- 2g = Rabi Frequency of a Single Photon
- Rate of **coherent exchange** between excitation of
***atom*** and ***field***

- g = dipole interaction strength between atom and cavity mode (of volume V)

- Strong Coupling Condition:

## Quantum Networks Enabled by Cavity QED

***Heart of the scheme:***
-  Single photon generation
- from one atom trapped in a cavity.

- Atomic internal states store quantum information locally,
- Cavity used for atom-field interaction

- Cirac *et al *PRL **78**, 3221 (1997)
- van Enk *et al* PRL **78**, 4293 (1997)

## Cavity QED with Trapped Atoms: Various Approaches

***Cavity QED with Trapped Atoms: Various Approaches***

- Our Scheme: Intracavity FORT

- Conveyor Belt for Single Atoms:  D. Meschede, Bonn

## Intracavity Far-Off-Resonance Trap (FORT)

- 	(Longitudinal modes only, i.e. L=nλ/2)

- 106

- Frequency

- 104

- 102

- n=95

- λF=935.6 nm

- 835.7

- 852.4

- Cs D2 line

- FORT

- Cavity Lock
- Laser

- Strong Classical
- Driving Field:
- ~ mW input
- ~ W inside cavity
- (~ 107 photons)

- Weak
- Driving Field:
- ~ 1 pW input
- <1 μW inside cavity
- (~ 1 photon)

- TRAPPING

- CAVITY QED

-  Possible to store atoms
- for seconds in this nearly conservative potential
-  Guaranteed overlap with CQED mode (in the transverse direction)

- FSR=
- 3 THz

## Trapping One Atom in the Cavity

***Trapping One Atom in the Cavity***

- Cloud of
- ~105 cesium atoms
- T=10-5 K

- Cooling beams

## Dipole Trap Overview for a Two Level Atom

- 	a.k.a. Far-Off-Resonance-Trap (FORT)

- Classical picture:  A dipole moment is induced in atom by optical field E
- Atom then sees a dipole force toward higher intensities I(r) (attractive for red detuning)

## Detailed calculation of Excited State Stark shifts: The picture is a bit more complicated...

**But... we can get some **
**Interesting answers.**

##  Cesium + 935 nm = A State-Insensitive Trap

-  Cesium + 935 nm = A State-Insensitive Trap

- Transition of interest nearly unshifted by trap:
- Cavity QED is then unperturbed by Stark shifts, which otherwise cause unwanted effective detunings

## Cavity QED “By the Numbers”

- J. McKeever, J. R. Buck, A. D. Boozer and H. J. Kimble, quant-ph/0403121

-  Atoms dropped into cavity with probe, side beams and FORT continuously on
-  Leads to interesting and useful effect

- Cooling

- Probe beam
- also recycles atom

## Demonstrated ability to resolve intracavity atom number in real time

- Typical trace (one event)

- Histogram built up from 500 events

- Steps in transmission always increase in time

- Scheme can be used to *prepare*
- specific atom number
- (although loading still probabilistic)

- See quant-ph/0403121 for details

## A One-Atom Laser in a Regime of Strong Coupling

- J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, and H.J. Kimble
- Nature, **425**, 268 (2003)

## Overview of Experiment

## One-Atom Laser –

- Observation of output vs. time

- Recorded Output
- 15000 / sec

- Background Counts:
- ~1000 / sec

- Avg. output vs. time
- for 2 values of atom flux:
- No significant change

## Experimental Data – Intracavity photon number <n> vs. pump I3

- Overall efficiency 
- Intracavity photon to TTL pulse
- 0.5*0.33*0.5*(4.3/7.2)

## Photon Statistics of the Emitted Light from the One-Atom Laser – 

- Investigate via measurements of the joint probability of photoelectric detection

## Intensity Correlation Function

## One-Atom Laser – Photon statistics from 4-state model

- <*n*>
*Q*
- g(2)(0)

## Intensity Correlation Function

## Distinctions from Prior Work

- _Distinctions from Prior Work_

## Summary – A One-Atom Laser in a Regime of Strong Coupling

- Comparison of theory & experiment: no time to discuss here, but there is reasonable agreement with data.  See quant-ph/0309133, and Suppl. Info.

-  Measurements of photon statistics exhibit photon antibunching (with
- inference of sub-Poissonian statistics) and are in reasonable* *accord with theory
-  Approximately stationary source of nonclassical light as a Gaussian beam

-  _Remaining issues –_
-  Measurements of optical spectrum of output
-  Cooling of axial motion – new scheme “invented” by D. Boozer; implement in lab
-  Determine atomic location along axial standing waves of FORT and cavity QED
-  ...

## Deterministic Generation of Single Photons from One Atom Trapped in a Cavity

- J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich and H. J. Kimble,
*Science ***303**, 1992 (2004)

- Convert one-atom laser to a pulsed excitation scheme in order to realize the basic building block of a quantum network

## Why Single Photons?

**Secure Quantum Cryptography**
-  Laser pulses containing nonzero multi-photon probability can leak information to an eavesdropper

***Why Single Photons?***
*Advantages over classical light sources*

**Linear Optics Quantum Computation** (Knill, Laflamme & Milburn, Nature **409**, 46 (2001)
-  Scheme for universal quantum computation requires only
**single-photon sources**, beamsplitters, phase shifters and detectors

**Quantum Networks**
- 	Use photons as carriers of quantum information

- This requires more than just photon production:
- Need to transfer local quantum states onto the field, and back.

## Single Photon Production

***Adiabatic Passage via Dark States***

- 

- 

- 

- 

- 

- 

- 5 s

- 1 s

- 10 s

***User-controlled pulse shapes***
***≈ ******100 ns ***

***Gaussian ***
***Spatial ***
***Mode***

## Experimental Results: Pulse shape and Efficiency

*OFF*

*Inferred total cavity output:*
- (69 ± 10)%

- Final detection efficiency about 3%

**14000** production attempts per trapped atom

- Efficiency?

- Consistent with
***100 %***
- intracavity production (±18%)
- (Based on measured mirror losses.)

## R=20.8 ±1.8

**Experimental**
**Results**

- Suppression of two-photon events:
**R=20.8 ±1.8**
- relative to a coherent state
***But***, worse than expected...

## Comparison of Intensity Autocorrelation Functions

- for Several Single-Photon Sources

- a) Single trapped atom – current work
- b), c) Quantum dot coupled to disc resonator – P. Michler *et al.*, Science **290**, 2282 (2000).
- d) Quantum dot coupled to vertical cavity – M. Pelton *et al.*, Phys. Rev. Lett. **89**, 233602 (2002).
- e) Freely falling cold atoms – A. Kuhn *et al.*, Phys. Rev. Lett. **89**, 067901 (2002).

- Inherently reversible
- for coherent transfer of
- quantum states

- Our values of R and efficiency compare favorably with other sources.

## R >150 

- Trapping time (seconds)

- R

**R >150 **
- at late times

- Using experimentally demonstrated scheme we can prepare **one atom** on demand.
- (quant-ph/0403121)

- Two-photon “contamination” is limited by ***rare ***events (about 3%) in which two atoms are loaded into trap

- Measure dramatic improvement in suppression factor R at long trapping times

## Single Photon Generation: Summary

- Single photons ***on demand*** with high efficiency
- (consistent with 100% inside cavity)

- Future Plans:
-  Reversibility
-  Indistinguishability
*** ******Quantum Entanglement of ***
***	******Distantly Separated Atoms***

- Output is highly non-classical:
**R >150**

- Scheme is ***coherent*** and ***reversible*** enabling implementation of ***quantum networks***

**14000** photons per trapped atom
- (improvements being made, **10****6** possible)

## What Next?

**2. Atomic motion (temperature)**
**	****	****Ideally would like to cool to the ground state of ****	****	****the axial motion**

**Still ahead:**
**	****Quantum schemes require control of all degrees of freedom**
**	****	****1. Internal state: **
**	****	****	****Control Zeeman sublevel via optical pumping and ****	****	****	****	****	****well-defined magnetic field**
** ****	****	****Should enable generation of polarized photons**

## Work in progress: Raman transitions

**  ****g1, g2 can be hyperfine levels (Zeeman sublevels) of Cs ground state**
**  ****coherently drive transitions between hyperfine ground states, like a two-level atom with no spontaneous emission**

**************= Raman laser (on-axis) **
********** ****= FORT! 2-in-1 laser**

**Work in progress: Raman transitions**
**A. D. Boozer, A. Boca, R. Miller, H. J. Kimble**

***A tool for manipulating the internal state of an intracavity atom,***
***and for implementing sideband cooling***

## H. Jeff Kimble

- (David Vernooy)
- (Alex Kuzmich)
- (Dan Stamper-Kurn)
- (Hanns-Christoph Nägerl)
**H. Jeff Kimble**

- (Joe Buck)
- (Ph.D. ‘03)

- Dave Boozer

- Russ Miller

- Andreea Boca

- Kevin Birnbaum
- Tracy Northup