►Coherent Stern-Gerlach splitting on an atom-chip

China, Sep 2013

Shimon Machluf

Ben-Gurion University of the Negev

www.bgu.ac.il/atomchip

S. Machluf, Y. Japha, R. FolmanNature Communications 4, 2424 (2013)

Views from the desert

OutlineOutline

• Motivation for interferometry on a chip

• Why Stern-Gerlach Interferometers should not work

• Our two level system

• Our Stern-Gerlach method

• Results

• Conclusions

What we want to do with chip interferometryWhat we want to do with chip interferometry

I: Surface physics – use the atoms as a probee.g. Mesoscopic transport, Johnson noise, shot noise of fractional charge

I: Surface physics – use the atoms as a probee.g. Mesoscopic transport, Johnson noise, shot noise of fractional charge

Non-interferometric atom-chip measurements

Example: electron transport

BGU+HD, Science (2008)

State of the art: RF and MW double-well splitting

II: Many bodye.g. Squeezing, collisional dephasing, thermodynamics

II: Many bodye.g. Squeezing, collisional dephasing, thermodynamics

e.g. an example of recent work done on an atom chip (Science, 2012)

PS single atom physicsis also still interesting! (x3)

III: momentum splitting for metrologyIII: momentum splitting for metrology

Ken Takase / Mark Kasevich 2008

e.g. Large area and large effective area

Could be used for sensing technology or fundamental studies:e.g. Chu, Holger Muller, Mark Kasevich

Fundamental tests with matter-wave interferometersFundamental tests with matter-wave interferometers

State-of-the-art in momentum splittingState-of-the-art in momentum splitting

Typically, accurate beam splitters are done with light: quantum accuracy (!) but hard to get large momentum

Is there an alternative, and can classical systems also do the job?

The differential force of the Stern-Gerlach experiment

Stern-Gerlach 1922

A plaque at the Frankfurt institute

commemorating the experiment

Stern-Gerlach in cold atoms @ BGU

Otto SternNobel prize 1943

Two reasons why aStern-Gerlach Interferometer

should not work

Two reasons why aStern-Gerlach Interferometer

should not work

1. External noise couples differently to different spin states

Heisenberg (1930), Wigner (1963): separation of the partialbeams will introduce a large dispersion of phases within theindividual beams.Bohm (1951), Englert (1988), Schwinger (1988), Scully (1989):The required precision is very high.

2. Is the wave packet like Humpty-Dumpty?

Quantum systems in our labQuantum systems in our labAlkali vapor Color centers in diamond

Find papers onthese 3 systemson our web site:www.bgu.ac.il/atomchip

The Atom Chip

Vapor work:

Archive 2013

Diamond work:

1-1 0

780nm

F=3F=2F=1F=0

1 20- 1-2F=2

F=15S1/2

5P3/2

Hyperfine structure of Rb 87

Zeeman sub-levels

6.8GHz

780nm

F=3F=2F=1F=0

1 20- 1-2

F=2

F=15S1/2

5P3/2

Lifting the degeneracy of the Zeeman sub-levels

6.8GHz

Same happens in the excited state

Pieter ZeemanNobel 1902

Stern-Gerlach in cold atoms @ BGU

780nm

F=3F=2F=1F=0

1 20- 1-2

F=2

F=15S1/2

5P3/2

Utilizing Rb as a 2-level system

6.8GHz

Same happens in the excited state

Second order Zeeeman

Two unique properties of the atom chip which we use here:

high field gradients and accurate on/off

Two unique properties of the atom chip which we use here:

high field gradients and accurate on/off

Example: I=2A r=10microns => B=400G => B’=40kG/mm

In addition, low inductance of wires enables quick on/off

Field gradient beam splitterField gradient beam splitter

•

•

•

•

•

•

(in our case: )

Gradient may be applied parallel or perpendicular to motion

Norman F. RamseyNobel prize 1989

Isidor Isaac RabiNobel prize 1944

Part we work with

Simple kinematic view:differential acceleration

A. Daniel et al., PRA (2013)

(< 10^6 A/cm^2)

Large distance

10^7 A/cm^2F=μ B’B[G]=2 I[A]/r[mm]

Geometrical factor for finite size:(2z/D)*arctan(D/2z)

Theory includes Breit-Rabi

GP sim.

Figure 1.1 – The Bloch sphere

Z

0

1

YX

Fourier transform view: varying Ramsey frequency

Data fromBGU

Experiment: free fallExperiment: free fall

• Single MOT atom chip experiment with BEC of 10^4 Rb^87 atoms

• atoms 100 μm from the surface of the chip

• Zeeman splitting of 25MHz

• Strong enough field to take the transition to the |2,0> out of resonance (250kHz)

• Two π/2 pulses with Rabi frequency 20-25 kHz

• Between the pulses, 2-3 A current in a 2x200 μm gold wire (< 10^6 A/cm^2)

• Measure momentum separation

Characterizing the beam splitter

Error bars are from different runs

The FGBS is very versatileThe FGBS is very versatile

• Large dynamic range

• Can split in the direction, and perpendicular to the direction, of motion

• Can work also in trapped mode for BEC or guided interferometry

• Can work also with the mag. insensitive clock states |1,0> ►|2,0> for low noise:

[ T ]

[ Hz ]

• If you put far away the second π/2, or two FGBS, you create a population interferometer

Choose your signal

spatial

population

Another example of versatility: trapped BECAnother example of versatility: trapped BEC

• Single MOT atom chip experiment with BEC of 10^4 Rb^87 atoms

• atoms 250 μm from the surface of the chip

• Trap frequencies 2π x 100 Hz and 2π x 100/1.4 Hz

• Zeeman splitting of 18MHz

• Strong enough field to take the transition to the |2,0> out of resonance (100kHz)

• Two π/2 pulses with Rabi frequency 5-10 kHz (pulses less accurate because of traps)

• Between the pulses, no need for current in the chip wire as traps give acceleration

• Measure momentum separation

vr

GP simulation with no free parameters

Error bars are from different runswith different Rabi frequencies and different TOF.

Bringing the wave packets togetherBringing the wave packets together• For the freely falling atoms, a second gradient is applied

• For trapped atoms, an oscillation time is added

All periodicities fit well with the known estimate:ht/md

1D BEC @ BGU: phase fluctuations –Self-induced interference pattern

Non deterministic fringes

Coherence = deterministic fringesCoherence = deterministic fringes

So why do we see coherence:

1. Wave packets very small2. Different spin for very short time3. And we are lucky that the initial positiondoes not matter

29 runs(1/2 an hourof data)

Outlook: ultimate phase stabilityOutlook: ultimate phase stability

General FGBS:

Our FGBS:

δΦ/ΔΦ , δp/Δp ~ δI/I, δT/T, δz/z

δp in our interferometer is canceledby the second pulse and is dependent on Δp which goes to zero.

δΦ within our FGBS:

If you plug in our 2A 5μs pulse, 100μm distance, δI/I=10^-3, you get δΦ=1 rad

δz/z may be made negligible e.g. in a 3 wire configuration where the trap position isindependent of current, but in any case as shown it affects only the c.m.degree of freedom.

Single shot: Calculate C(t). For BEC C(t)=1 so visibility should be 100% pending purity, population imbalance, imaging resolution, etc.

Shot-to-Shot:

δp/Δp: 10^-7 and beyond.

Comment on trapped BEC

Side remark: A separate project by Shuyu ZhouSide remark: A separate project by Shuyu Zhou

Shuyu explaining his experimentto Peter Zoller and Ignacio Cirac

Quantum coherence in a collision between a BEC and a snake shaped wire

Very preliminary results of phase imprint

Average of 30 images

Shimon Machluf

• The field gradient beam splitter is fast, allows large momentum,is very versatile, and requires no light

• Atom Chips enable the strong pulsed gradients this beam splitter requires

• Applications range from many body, to surface\material science, and metrology.

• We have seen first signs of coherence. We are still very far from shot noiseso there is much to improve.

• It seems that for high momentum transfer, the SG beam-splittermay even have better accuracy than light beam-splitters, but itsstill very early to tell…

To conclude:

My latest anti-gravity experiment….

Pieter ZeemanNobel 1902

A field gradient will produce a force on any magnetic moment

first and secondorders

No two separate wave packets

0

0.25

0.5

0.75

1

0 1 2 3 4 5 6

time

P1(

t)

0

Figure 2.1 – Rabi oscillations

2

2

0

2

220

2

01 ωωΩΩ~

,tΩ~

cos1Ωωω

Ω

2

1(t)P1(t)P

Isidor Isaac RabiNobel prize 1944

Rabi Oscillations in a 2-level system:

π/2 pulse

Bloch sphere

Figure 1.1 – The Bloch sphere

Z

0

1

YX

12

θsine0

2

θcosΨ i

Examples:

Cold atoms @ BGU

Room temperatureatoms in a solid (!) @ BGU

Additional tools we will use:Additional tools we will use:

Bloch sphere

Figure 1.1 – The Bloch sphere

Z

0

1

YX

12

θsine0

2

θcosΨ i

Norman F. RamseyNobel prize 1989Ramsey fringes

022 )()( BFREERAMSEY TT

T

RAMSEYZ dttT0

, ))(cos(cos)(

0

0.2

0.4

0.6

0.8

1

0 5 10T

P1

Detuning =0

Detuning =0.1

Detuning =0.5`

RamseyOscillations@ BGU

Norman Ramsey (Nobel 1989, passed away 2011) and Dan Kleppner - 2005

Atom chip review article: RF et al. Adv. At. Mol. Opt. Phys. 48, 263 (2002)

One of the humble beginnings: RF et al. PRL 84, 4749 (2000)

Applications: clocks, acceleration sensors, gravitational sensors, magnetic sensors, quantum memory and communications, quantum computing

Fundamental science: Decoherence, interferometry, many body, atomic physics,low dimensional systems, atom-surface physics, surface physics, symmetries and fundamental constants

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hA quick reminder of what the atom chip is:

“where material engineering meets quantum optics”

A quick reminder of what the atom chip is: “where material engineering meets quantum optics”

The monolithic integration dreamThe monolithic integration dream

The atom chip technology is advancing very rapidly so that eventually, all the different particles such as Rydberg, molecules, atom-like (NV), ions, cold electrons, etc. may be put on the chip, including entanglement to a quantum surface.

Atom

Chips:

From

3 in 2000 to ~30 today,

• new book on atom chips, RF, Philipp Treutlein and Joerg Schmiedmayer, (Eds: Jakob Reichel and Vladan Vuletic)

• special issue on QIP (Journal of Quantum Information ProcessingEditors :Howard Brandt & RF )

The Atom Chip definition is broadeningThe Atom Chip definition is broadening

More information on the atom chip in:More information on the atom chip in:

+ near field optics, plasmonics, etc.

Highest tem

perature gradient know

n to mankind

Ion and permanent magnet chips@ BGU for Mainz and Amsterdam

A Bose-Einstein CondensationA Bose-Einstein Condensation

1D BEC @ BGU: phase fluctuations –Self-induced interference pattern

3D BEC @ BGU

Phase Imprint

What is phase imprint?

The Process of Phase Imprint

Ucu_Z + Usnake1

Ucu_Z + Usnake2

Icu_Z =32.3A

Isnake1 =30mA

Isnake2 =5mA

Iy_bias =84.7A

Ix_bias =0A

We suddenly reduced the snake current from 30mA to 5mA. The BEC approached the chip surface and came back. After 6ms, about one oscillation cycle, we turned off all currents and released the BEC.After about 9-13ms we probe the density distribution by absorption imaging.

About 38um

About 5um

Experiment result of phase imprint __single shot

Stability_Average of 30 shots