1. Preparation, manipulation and detection of single atoms on a chip
Guilhem Dubois
Supervisor: Jakob Reichel
Atomchips group, Laboratoire Kastler Brossel, ENS Paris

2. Single atoms : remarkable features
Tcoh > 10s
Well-controlled system!
Testbed for Quantum Mechanics
Qubit candidate?
Cooling & trapping
single atom characterized by a quantum structure of levels, which is perfecly known
if you add the 3 external dof, it is still a simple quant system
Stable states+ mw transitions
Tc limited by B field inhomogeneity
Laser cooling, magnetic and optical traps
Scalability: array of magnetic microtraps / optical lattices
manipulate single, identical atoms in parallel. 2

3. Outline Introduction: experiments with single atoms
Cavity QED and single atom detection
Experimental setup
Detection of waveguided atoms
Preparation and detection of trapped single atoms
Detection with minimum backaction
Quantum Zeno effect

4. Single atoms toolbox Preparation Interaction Detection 4
Terminology of QIP
2-qubit -> entanglement 4

5. Single atoms toolbox Preparation Interaction with … Detection
light fields (in free space, in a cavity)
 atom-photon entanglement [Volz et al. PRL 96 (2006)]  non-classical states of light - Fock states [Deleglise Nature 455 (2008)] - polarisation-entangled photons [Wilk Science 317 (2007)]
another single atom (atom-atom entanglement)
 controlled collisions [Mandel et al. Nature 425 (2003)]  Rydberg blockade [Gaëtan et al. Nat. Phys. 5 (2009)]
Terminology of QIP
2-qubit -> entanglement 5

6. Single atoms toolbox
Preparation : constraints  deterministic  specific internal state e.g. clock states  specific motional state e.g. trap ground state
Interaction
Detection
Here the preparation step is not step not easy
difficult to have exactly one atom in a given trap
furthermore constraints depend on the exact experiment you want to achieve, but are generally of two forms : either you want to single out a specific internal state, like « clock states » which have long coherence time, and/or aim for a specific motional state, like the ground state of the trap. 6

7. Single atoms toolbox
Preparation : feedback  deterministic  specific internal state e.g. clock states  specific motional state e.g. trap ground state
Interaction
Detection : here atom counting  minimum backaction (spontaneous emission)
Terminology of QIP
2-qubit -> entanglement
How can we achieve that ? 7

8. Outline Introduction Cavity QED and single atom detection
Experimental setup
Detection of waveguided atoms
Preparation and detection of trapped single atoms
Detection with minimum backaction
Quantum Zeno effect

9. Atom-cavity system e b Strong coupling regime : g >> k , g
optical
cavity k
coupling g
Schematic atom+ cavity
Coupling rates and decay rates
Strong coupling regime.
Strong coupling regime : g >> k , g
 small mode volume
 good quality mirrors

10. Cavity QED experiments
 single atom - single photon interaction
Detection of single atoms
Oettl et al. PRL 95 (2005)
Quantum light sources
Hijlkema PhD thesis (2007)
Evidence of field quantisation & photon counter
Brune et al. PRL 76 (1996)
The experiments you can perform with a cavity QED system take advantage of the good control and the large value of the single atom – single photon interaction.
1- In the experiments of Haroche group at ENS, the atom acts as a probe of the cavity field, and allows to count the number of photons in the cavity. It is the oscillations frequency of the atom which tells you how many photons are in the cavity. This expt is actually a very nice proof of field quantisation.
2- The subject of a number of recent expts is to take advantage of the good control over the coupling to fashion the light-matter interaction and obtain sources of quantum light. Here I show of expt from the MPQ group which produces single photons on demand from a trapped atom in a cavity.
3- Another class of experiment you can perform with an atom-cavity system is the detection of single atoms, for example here I show an expt performed in Zurich where they use the detector to probe the coherence properties of an atom laser beam.
I should now get into more detail about the way a cavity is used to detect single atoms.

11. Resonant Jaynes-Cummings spectrum
b,0
e,0
energy
b,1
b,0
+,1
energy
coupling g
-,1
splitting 2g e b
Interaction single atom - single photon visible!
Now we consider the situation when the atom and the cavity mode are exactly resonant.
The interaction between the atom and the cavity field is described by a simple Hamiltonian which models the coherent energy exchange between the atom and the cavity.
Initially the level structure is like that, with a degeneracy between the atomic excited state and the one-photon state.
2-The effect of the coupling is to lift this degeneracy to obtain new eigenstates of the system called the dressed states.
3- this interaction with a single atom is visible in the transmission spectrum of the cavity as the initial transmission peak is splitted in two new peaks corresponding to the position of the dresses states.

12. Principle of single atom detection in a cavity
Optimum measurement rate 1 measurement = 1 photon
With losses L : ¡signal = L £ ¡inc
1-The detection process with a strongly coupled cavity is optimum.
I just need 1 photon to know if I have one atom or not.
Or equivalently: if I have a single atom in the cavity, that can be in two state, one resonant one nonresonant, I would just have to send one photon to know in which state it is.
If I had a single photon source, I would just need to trigger it once.

13. Detection with minimum backaction?
 Backaction characterized by Gsp
For a free space detector:
factor C !
Now if you look again at this picture, there is something quite fascinating (and suspicious)
: you can detect the atom with light, but there is no light entering the cavity. We would therefore say that the detection is done with no spontaneous emission, no perturbation of atomic variables like motion, zeeman state, etc.
In reality, there is always some light that enters the cavity, and you get some spontaneous emission in the external modes of the light fields (shown in green here). Nevertheless we can still compute it and find that the fraction of light that is scattered by the atom out of the cavity, compared to the light we sent in in very small : 1/C
Let us know insist on the differences with a free space based detection scheme, such as fluorescence detection. Here, the signal that you get in olny due to spontaneous emission, and for the same signal, you have a factor C of difference between free space and cavity detection. The idea is then to make this factor as big as possible to obtain the smallest possible backaction on the atom.

14. Outline Introduction Cavity QED and single atom detection
Experimental setup
Detection of waveguided atoms
Preparation and detection of trapped single atoms
Detection with minimum backaction
Quantum Zeno effect

15. AutoCAD’s view Integrated atom chip-cavity system
The experimental setup consists in the combination of an atom chip, used to trap ultracold atoms, and a high-finesse Fabry-Perot cavity

16. Atom chip basics 1cm Applications: - BEC
- precise transport and positioning
- atomic clocks and interferometers
- single atom manipulation?
Magnetic traps:
- versatility
- strong confinement close to the surface
Atomchips are used to trap atoms, with magnetic fields. They are made of small wires, here it’s gold wires, on a planar surface, in which you drive current to create a magnetic trap, together with external bias fields.
Many wires -> many trap configurations.
Small distance atoms/chip -> good confinement. -> applications …

17. Miniaturized Fabry-Perot cavity
Mention this cavity is OUR design
C02 laser ablation -> good surface quality, curved fiber tips -> HR coating

18. Miniaturized Fabry-Perot cavity
- tunable
- small mode volume w0=4 mm ; d=39 mm
- integrated 150mm from chip surface
Cavity QED
Strong coupling regime!
finesse F = 38000
coupling g /2p = 160 MHz
cavity decay k / 2p = 50 MHz
atomic decay g / 2 p = 3 MHz
cooperativity C = g2/2kg = 85
Mention this cavity is OUR design

19. Outline Introduction Cavity QED and single atom detection
Experimental setup
Detection of waveguided atoms
Preparation and detection of trapped single atoms
Detection with minimum backaction
Quantum Zeno effect

20. Detection of waveguided atoms Principle
APD
BEC
Atomic waveguide a
Mention it is the easiest way to put SINGLE atoms in the cavity
Detection zone
LASER
… the easiest way to put SINGLE atoms in the cavity

21. Detection of waveguided atoms
Reference with no atoms

22. Detection of waveguided atoms
Single run with atoms

23. Detection of waveguided atoms Experiment
Threshold
Excellent signal to noise ratio for dilute BECs.
From these results : not possible to conclude on a detection efficiency with this technique.
Some atoms are missed – because they do not lead to a deep enough signal.
 these are single atoms !!!

24. Outline Introduction Cavity QED and single atom detection
Experimental setup
Detection of waveguided atoms
Preparation and detection of trapped single atoms
Detection with minimum backaction
Quantum Zeno effect

25. Trapping & detecting the atoms in the cavity mode
Transfer magnetic trap  Optical dipole 830nm
Experiments with BEC : see Colombe et al. Nature 450 (2007)

26. Positioning the BEC in the cavity
BEC in magnetic trap
N ~ a few 1000s
input fibre
output fibre
Initial cloud size ~1mm  single-site loading possible. Y
Dipole trap
@ 830nm
Probe light
@ 780nm

27. Vacuum Rabi Splitting with collective enhancement
How to get to the single atom regime?
Laser detuning ΔL-A [GHz]
The effect of a BEC in a cavity in to increase the coupling by srqt(N) compared to a single atom. We measured this increased coupling by performing a spectroscopy of the system for different values of N, and looking for the resonance peaks corresponding here to the collective dressed states. We find a very good agreement to the theory.
2-We also see on this curve that is difficult to get to the small atom number regime. So how can we prepare trapped single atoms this way?
Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger and J.Reichel Nature 450 (2007)

28. From the BEC to just a single atom
Problem: Evaporation down to N=1 not possible.
Solution: Extract a single F=2 atom from a ‘reservoir’ of F=1 atoms – and detect it.
F'=0,1,2,3
Cavity tuned to F=2 -> F’=3 transition
F=2
F=1
Reservoir (N~10)
Weak MW pulse GHz)
~2% transfer probability/atom
To do deterministic preparation of single atoms with cavity , you need to start with a very small could of 0 or a1 toms.
Noise in external magnetic fields and current wires.
Key idea: weak mw pulse to decrease the relative probability of multiple transfers.

29. Usual strategy to obtain trapped single atoms
“Wait and trap” scheme:
dip !
First trapped cavity QED experiments (Caltech, Garching)
Problem: the atom is hot - cooling required (Raman sideband cooling, cavity cooling)
Possible improvement: optical conveyor belt (Bonn, Zurich)
We do differently! We aim at direct preparation in the trap ground state
Analogy with our scheme : position  internal state.

30. “Preparation and detection” iterative sequence
time
Reservoir
preparation mw
Detection mw
Detection
Etc …
F’=3
F=2
F=1
1000
~10

31. 0 or 1 atom in F=2?
nAPD ~ 25
nAPD < 1

32. Analysis of detection pulses
Transfer efficiency 10%
Relative transmission 1.4%
threshold
We find that the results of detection pulses, in terms of APD counts, are distributed along a Bi-Poissonian distribution
successful transfers (~10%)
unsuccessfultransfers (~90%)
after ~10 pulses  Reliable preparation

33. Lifetime of the atoms during detection
single run or ??

34. Lifetime of the atoms during detection
Fit or ??
Average lifetime 1.2 ms
Limited by depumping to F=1
Fidelity=99.7%
+ QND measurement
stat. limit
depump limit

35. Outline Introduction Cavity QED and single atom detection
Experimental setup
Detection of waveguided atoms
Preparation and detection of trapped single atoms
Detection with minimum backaction
Quantum Zeno effect

36. How can we measure spontaneous emission?
Zeeman “random walk”:
But not visible in lifetime !

37. Measurement and preparation of a specific Zeeman state (F=2;mF=0)
Measurement of mF p p p
Until now I did not talk about Zeeman state
Zeeman state : not visible in cavity detection
+ all Zeeman states are trapped
-> however it is important to perturb the atomic state as little as possible
for preparation in the ground state, for example, or a given Zeeman state. B

38. Diffusion in the Zeeman manifold
Fit

39. Detection figure of merit : backaction
 Better than a perfect free space detection !
 Possible to prepare a single atom without changing the motional state !
Improvements require:
- simultaneous R&T meas.
- lower optical losses

40. Detection without perturbation ?
with L ~ 0.1 : C ~ 20
expected value C ~ 85 ???
What is the real measurement rate of the system?
for a lossless observer ¡m = ¡inc = C ¡sp
can we check that ???

41. Outline Introduction Cavity QED and single atom detection
Experimental setup
Detection of waveguided atoms
Preparation and detection of trapped single atoms
Detection with minimum backaction
Quantum Zeno effect

42. Quantum Zeno Effect b mw p a m = Coherence decay rate between a and b
Cavity & atomic
excited state
F=2;mF=0
F=1;mF=0 b
mw p
What does the QZE consist in? Consider the situation of two stable states, between which you can drive a Rabi oscillation with an external field.
Now suppose that you continuously measure the population in one of the two states, for example by coupling to a fast-decaying 3rd state. This measurement will actually prevent the transitions between the two initial states. The reason is that in QM, the measurement perturbs the state. More precisely, the measurement destroys the coherence between the two states, which are necessary to establish the Rabi osc. Therefore, if you apply a pi-pulse on the initial transition, you find that the transfer probability will drop from 1 to 0 as you increase the meas rate.
In the experiment, the transition we consider is the F=2 mF=0 -> F=1 mF=0 transition, and the measurement is performed by pumping the cavity which measure the value of F. The measurement rate is in fact the coherence decay rate of an initial state superposition.
Here, we find that the coherence decay rate = photon input rate in the cavity mode;
If we compare with the Zeeman diffusion expt. we find that this is approx 20 times larger than sp em rate.
It is also equal to the optimum detection rate for the experimentator, if the system were lossless.
So this expt actually demonstrates that the state of the system is measured (at least by the environment) with almost no sp. em. a
m = Coherence decay rate between a and b
m = Photon input rate
~ 20 £ Spontaneous emission rate

43. Summary Preparation of trapped single atoms starting from a BEC:
preparation in a specific Zeeman state  qubit clock states
well localized within the cavity
First detector of single atoms on a chip  ability to distinguish F=1 from F=2 states with 99.7% fidelity
Demonstrated a Quantum Zeno effect w/o spontaneous emission.

44. Outlook e laser cavity b a
Characterize the atomic motional state are we still in the ground state?
Manipulate of pairs of atoms in the cavity
 Cavity-assisted entanglement generation
Combine with other atom chip technology (state dependent mw potentials)
Quantum memory with BEC and Fiber-cavity
- Large collection efficiency
- Long storage time
laser
cavity a b e

45. Single atom Vacuum Rabi splitting

46. Atomchip-based single atom detectors
Fluorescence (Wilzbach et al )
Photoionization (Stibor et al PRA 76 (2007))
Cavity QED (Purdy et al. APB 90 (2008)) 1 2 3

47. Single atoms – light/matter interface
laser
vacuum a b e
Single photon source
Atom-photon entanglement
Photon-photon entanglement
Long-distance atom-atom entanglement via entanglement swapping  Quantum networks for quantum cryptography
- Probabilistic is OK (DLCZ 2002)
 atomic ensembles possible but coherence time ~ms.
- Collection efficiency small with single atoms
 a cavity helps
Lambda scheme

48. Single atom ‘temperature‘
Release and recapture
Mean energy < 100 mK
(trap depth 2.6 mK)

49. Single atom Rabi oscillations

50. Single atoms : some fascinating achievements
Beugnon et al.
Nature 440 (2006)
Hong-Ou-Mandel effect
Evidence of field quantisation & photon counting
Brune et al. PRL 76 (1996)
Massive multi-particle entanglement
Mandel et al. Nature 425 (2003) 50

51. Single atoms toolbox Preparation & trapping 1-qubit gates
State readout
Scheme : controlled collisions
Entangle atomic internal and external state
Theory:
Calarco et al. , PRA 61 (2000)
Experiment:
Mandel et al. Nature 425 (2003)
Böhi et al. preprint arXiv
for this entanglement to succeed you need a perfect knowledge about the state initial state
-> trap grd state!
Requirements:
- state dependent potentials
- preparation in the trap ground state 51

52. Single atoms toolbox Preparation & trapping 1-qubit gates
State readout
Scheme : Rydberg gate r b
d1.d2 a
Theory:
Jaksch et al. PRL 85 (2000)
Experiment:
Wilk et al. preprint arXiv:
Ref : Calarco proposal
Bloch realization
Requirements:
- preparation of Rydberg states
- small distance (<5mm) between atoms 52

53. Single atoms toolbox Preparation & trapping 1-qubit gates
State readout
Scheme : cavity-mediated interaction ae ea
aa+1 photon g g ba ab aa aa
You et al. PRA 67 (2003)
Ref : proposal You and Li
Requirements:
- optical cavity, strong coupling regime
- good control over the coupling g 53

54. Single atoms toolbox Preparation & trapping 1-qubit gates
State readout :
For free space detection Signal = Spontaneous emission  heating & depumping
Non-destructive measurement?
- Not necessary in principle
- but very useful for preparation! e
QND measurement ->
Not necessary for quantum computing
BUT allows to do preparation in a well-defined state with active feedback.
 need a cavity to enhance light/matter coupling and avoid spontaneous emission b a 54

55. Detection of waveguided atoms Analysis
Spontaneous emission:  depumping to untrapped states.
Some atoms lost before they reach maximum coupling
Still: Demonstrates >50% efficiency single atom detection (absorption imaging, simulations)
But: trapped atoms in the strong coupling region should lead to better results