and nanomechanical resonators on an atom chip

physik.lmu.de

and nanomechanical resonators on an atom chip

Ultracold atoms coupled to micro- ong>andong>

ong>nanomechanicalong> ong>resonatorsong> on an atom chip

Philipp Treutlein

D. Hunger, S. Camerer, T. W. Hänsch (MPQ/LMU Munich)

D. König, J. P. Kotthaus (LMU Munich), J. Reichel (ENS Paris)


Quantum optics meets condensed matter

Quantum optical systems + condensed matter concepts:

Ultracold atoms in optical lattices:

“artificial condensed matter system”


Quantum optics meets condensed matter

Quantum optical systems + condensed matter concepts:

Ultracold atoms in optical lattices:

“artificial condensed matter system”

Condensed matter systems + quantum optical concepts:

Superconducting circuits, quantum dots:

“artificial atoms”

Laser cooling of mechanical oscillators


Quantum optics meets condensed matter

Quantum optical systems + condensed matter concepts:

Ultracold atoms in optical lattices:

“artificial condensed matter system”

Condensed matter systems + quantum optical concepts:

Superconducting circuits, quantum dots:

“artificial atoms”

Laser cooling of mechanical oscillators

Quantum optical systems + condensed matter systems:

Atom chips provide an interface

between ultracold atoms ong>andong>

solid-state systems on a chip


Atom chips: quantum gases meet the solid state

atomic Bose-Einstein

condensate (BEC)

10 – 10 4 atoms

T ~ 500 nK

500 nm

variable distance

100 nm – 100 μm

gold wires for

atom trapping

nanodevice

microfabricated chip

T = 300 K


Interactions between two very different systems

Bose-Einstein

condensate

Chip-based microong>andong>

nanostructures


Interactions between two very different systems

Bose-Einstein

condensate

Chip-based microong>andong>

nanostructures

manipulate

„Quantum laboratory for atoms on a microchip

• simple path to BEC ong>andong> Fermi degeneracy

• compact clocks ong>andong> interferometers

• quantum gases in tailored potentials (double well, 1D, ...)

• cavity QED on a chip

• quantum information processing

• BEC entanglement


Interactions between two very different systems

Bose-Einstein

condensate

Chip-based microong>andong>

nanostructures

probe

„Quantum AFM tip“

• study atom-surface interactions

• microscopy of magnetic, electric, or microwave fields

• monitor dynamics of on-chip mechanical ong>resonatorsong>,

nanomagnets, Josephson junctions, ...


Interactions between two very different systems

Bose-Einstein

condensate

Chip-based microong>andong>

nanostructures

strong interactions

„Hybrid (quantum) systems“

• coherent exchange of quanta

• laser-cooled atoms as a refrigerator (nK base temperature...)

• hybrid measurement devices (magnetic field sensor,...)

• hybrid quantum information processors

• fundamental studies of entanglement ong>andong> decoherence


Outline

Atom chips

• basic concepts

• experimental setup

• BEC preparation

Ultracold atoms near the chip surface

atom-surface interactions

• coherent manipulation ong>andong>

coherence lifetime

BEC coupled to micro- ong>andong>

ong>nanomechanicalong> ong>resonatorsong>

• coupling via surface potential

• magnetic coupling:

a mechanical cavity QED system


The wire trap

atoms are trapped in

B-field minimum

magnetic field

of currentcarrying

wire

homogeneous

field

trap (2D)

wire

Zeeman Hamiltonian:

Wire field:

Wire field gradient:

weak-field seeking state: g F

m F

> 0


Chip-based wire traps

Microfabricated wire on a chip:

2D atom guide

Wire crossing: „dimple-trap“

harmonic confinement in 3D

B-field

atoms

Benefits of integration on chip:

• small wires - high trap

frequencies: up to 1 MHz

• small atom-surface distance:

< 1 μm possible

• complex, tailored potentials

through microfabrication


State of the art: multi-layer atom chips

70 μm

5 cm

Au (1 μm)

Si chip

AlN carrier chip

polyimide (6 μm)

Au (5 μm)

epoxy

Au (10 μm)


State of the art: multi-layer atom chips

70 μm

5 cm

Au (1 μm)

Si chip

AlN carrier chip

polyimide (6 μm)

Au (5 μm)

epoxy

Au (10 μm)


State of the art: multi-layer atom chips

70 μm

5 cm

20 μm


State of the art: multi-layer atom chips

70 μm

5 cm

We gratefully

acknowledge the

Kotthaus group at CeNS,

LMU Munich for

cleanroom access

20 μm


Compact glass cell vacuum chamber

water cooling

wire connectors

copper block

3.5 cm

atom chip with

mirror surface

base pressure

in glass cell:

3 × 10 -10 mbar

at T = 300 K

(trap lifetime ∼ 5 s

with dispenser on)

Rb dispenser

to ion pump


Production of Bose-Einstein condensates

multi-step

sequence:

• mirror-MOT

• optical molasses

•optical pumping

• magnetic trap

• transport atoms

• evaporative cooling

to BEC

d

all inside the

same glass cell

experimental

cycle: 10 s


Absorption imaging

image shadow cast by

atoms onto CCD camera

detection beam

lens

CCD camera

chip surface

BEC

d = 50 μm

absorption image


Bose-Einstein condensation on an atom chip

absorption images

of atomic density

T > Tc

evaporative cooling

BEC of

10 4 atoms

in |1,-1i

thermal

ensemble of

bosons

T ≈ Tc

T ¿ Tc

Bose-Einstein

condensate


Outline

Atom chips

• basic concepts

• experimental setup

• BEC preparation

Ultracold atoms near the chip surface

atom-surface interactions

• coherent manipulation ong>andong>

coherence lifetime

BEC coupled to micro- ong>andong>

ong>nanomechanicalong> ong>resonatorsong>

• coupling via surface potential

• magnetic coupling:

a mechanical cavity QED system


Ultracold atoms close to a “hot“ surface

Loss, heating ong>andong> decoherence


Atom-surface interactions

Previously unexplored area of atom-surface physics

Theory: C. Henkel et al., 1999-2003

Experiments: London, Boulder, Stanford, MPQ/LMU

1. Thermal magnetic near-field noise

magnetic dipole

moment of atom

fluctuating magnetic fields

due to thermal motion of

electrons in chip conductors

Spin flips (loss) + decoherence


Atom-surface interactions

Previously unexplored area of atom-surface physics

Theory: C. Henkel et al., 1999-2003

Experiments: London, Boulder, Stanford, MPQ/LMU

1. Thermal magnetic near-field noise

magnetic dipole

moment of atom

fluctuating magnetic fields

due to thermal motion of

electrons in chip conductors

Spin flips (loss) + decoherence

2. Attractive surface potential

• van der Waals/Casimir-Polder potential

• Potential due to surface adsorbates

electric polarizability

of atom

(fluctuating) electric

dipoles in surface

potential

V m

V m

+V s

Loss due to reduced trap depth

distance to chip surface


Coherence close to the surface

Hyperfine sublevels of 87 Rb with

identical magnetic moments

P. Treutlein et al., Phys. Rev. Lett. 92, 203005 (2004).

rf

|1〉 = |F=2,m F

=+1〉

F = 2

mw

|0〉 = |F=1,m F

=-1〉

F = 1

m F

= -2 -1 0 1 2

“Qubit states“ of 87 Rb

• both magnetically trappable

• nearly identical potentials

• long coherence lifetime


Coherence close to the surface

P. Treutlein et al., Phys. Rev. Lett. 92, 203005 (2004).

Hyperfine sublevels of 87 Rb with

identical magnetic moments

Coherence lifetime measurement

(Ramsey sequence, atom-surface distance: 9 μm)

rf

|1〉 = |F=2,m F

=+1〉

F = 2

mw

|0〉 = |F=1,m F

=-1〉

F = 1

m F

= -2 -1 0 1 2

“Qubit states“ of 87 Rb

• both magnetically trappable

• nearly identical potentials

• long coherence lifetime


Coherence close to the surface

P. Treutlein et al., Phys. Rev. Lett. 92, 203005 (2004).

Hyperfine sublevels of 87 Rb with

identical magnetic moments

Coherence lifetime measurement

(Ramsey sequence, atom-surface distance: 9 μm)

rf

|1〉 = |F=2,m F

=+1〉

F = 2

mw

|0〉 = |F=1,m F

=-1〉

F = 1

m F

= -2 -1 0 1 2

“Qubit states“ of 87 Rb

• both magnetically trappable

• nearly identical potentials

• long coherence lifetime


Plenty of room for applications

•Atomic clock on a chip

P. Treutlein et al.,

PRL 92, 203005 (2004).

•Atom interferometer

•On-chip quantum gates

|1i

|0i

P. Treutlein et al.,

PRA 94, 022312 (2006).

P. Treutlein et al.,

Fortschr. Phys. 54, 702 (2006).


Minimum atom-surface distance

Potential above Si surface

ω t /2π = 1 kHz

Casimir-Polder surface potential V s

lowers trap depth to V b

(d).

Minimum atom-surface distance d m

depends on trap frequency ω t

ong>andong>

on tolerable minimum trap depth.


Outline

Atom chips

• basic concepts

• experimental setup

• BEC preparation

Ultracold atoms near the chip surface

atom-surface interactions

• coherent manipulation ong>andong>

coherence lifetime

BEC coupled to micro- ong>andong>

ong>nanomechanicalong> ong>resonatorsong>

• coupling via surface potential

• magnetic coupling:

a mechanical cavity QED system


Micro- ong>andong> ong>nanomechanicalong> ong>resonatorsong>

Mechanical cantilever (Si, SiN, ...)

Fundamental resonance:

t

l

w

a(t)

S. Camerer, LMU

(collab. Hänsch/Kotthaus)


A gas of atoms as a refrigerator


A gas of atoms as a refrigerator

laser-cooled atoms

„base temperature“ < 1 μK

⇒ cool the resonator to the ground state


A gas of atoms as a refrigerator

laser-cooled atoms

„base temperature“ < 1 μK

⇒ cool the resonator to the ground state

Yes, if ...

... strongly coupled

... to a single mode

... of a small resonator

... with low damping


Proposals for hybrid quantum systems

Theoretical proposals involving atoms/ions/molecules

ong>andong> mechanical ong>resonatorsong>

paper system coupling

D. J. Winelong>andong> et al., J. Res. NIST 103, 259 (1998). ion electrostatic

L. Tian et al., PRL 92, 247902 (2004). ion electrostatic

W. K. Hensinger et al., PRA 72, 041405 (2005). ion electrostatic

D. Meiser et al., PRA 73, 033417 (2006). atoms optical

P. Treutlein et al., PRL 99, 140403 (2007). atoms magnetic

C. Genes et al., arXiv:0801.2266 (2008). atoms optical

H. Ian et al, arXiv:0803.0776 (2008). atoms optical

K. Hammerer et al., arXiv:0804.300 (2008). atoms optical

S. Singh et al., arXiv:0805.3735 (2008). polar

molecules

electrostatic

X. X. Yi et al., arXiv:0807.2703 (2008). atom optical

...


Coupling mechanisms

coupling via surface potential

coupling via optical lattice

magnetic coupling


First experiment: commercial AFM cantilever

SiN cantilever:

L = 200 μm,

W = 40 μm,

T = 600 nm

Au+Cr mirror,

thickness 65 nm

resonance frequency:

ω r

/2π = 10.0 kHz

quality factor:

Q = 1600

200 μm


Calibration of cantilever amplitude

Beam deflection readout:

- laser focused on cantilever tip

- driven cantilever

(20mVpp)

- thermal cantilever

- beam deflection detected with

quadrant photodiode

- signal recovered with two channel

Lockin amplifier

resonance parameters

resonance frequency 10kHz

Q factor 1655

driving efficiency 31.1nm/V


Atom chip with AFM cantilever

MOT region

w/ dielectric mirror

wire bonds

piezo for

actuation

spacer

AFM cantilever

chip

base chip

experiment chip


Atom chip with AFM cantilever


Magnetic trap close to cantilever


Magnetic trap close to cantilever

cantilever support

cantilever

d=120 μm

2 × 10 3 atoms


Atom preparation close to cantilever


Atom preparation close to cantilever

d


Atom preparation close to cantilever

d

Casimir-Polder surface potential:

decreases trap depth loss of atoms

remaining fraction of atoms:

χ =

1−

exp( −U / k B

T )

sudden loss of Boltzmann tail,

see Lin et al., PRL 92, 050404 (2004).

(hold time: 1 ms)

U

µ c


Coupling atoms to cantilever motion


Coupling atoms to cantilever motion

Oscillating cantilever modulates:

barrier height → atom loss

trap position → drives c.o.m. oscillation

trap frequency → heating


Detection of cantilever resonance with atoms

atoms

a

piezo-driven cantilever:

oscillation amplitude:

resonance frequency:

a ~ 100 nm r.m.s.

ω r /2π = 10.0 kHz

6 Hz

atom trap parameters:

atom-surface distance: d = 760 nm

trap frequency: ω t /2π = 10.5 kHz

thermal ensemble T = 1.4 T c


Dependence of signal on atom-surface distance

• drive cantilever on resonance

• scan atom-surface distance

contrast

SNR

a=62nm


Parametric resonance

• Fixed piezo driving strength ong>andong> frequency

• Piezo drive set on cantilever resonance (a = 80 nm)

• Scan trap frequency

frequency of

cantilever

cantilever drives

transitions between

trap states


Trap spectroscopy with the cantilever

cantilever drives

transitions between

trap states


Coupling via Casimir-Polder potential

Summary:

atom-surface distance < 1 μm required

• parametric resonance is the dominant

coupling mechanism

• coupling depends sensitively on trap

parameters → control

Future experiments:

• coupling to carbon nanotubes


Coupling mechanisms

coupling via surface potential

coupling via optical lattice

magnetic coupling


Coupling via optical lattice


Coupling via optical lattice

Optical lattice provides coupling

over long distances!


Coupling via optical lattice

• long-distance coupling

anharmonicity of lattice

isolates two-level system

• detect atomic state via

shape of wave function

Spielman et.al.: PRA 73 (2006)


Coupling mechanisms

coupling via surface potential

coupling via optical lattice

magnetic coupling

P. Treutlein et al., PRL 99, 140403 (2007).

related work: J. Kitching (NIST),

PRL 97, 227602 (2006).


Nanomechanical resonator with a magnetic tip

Si

Si cantilever fabricated on SOI chip

Co

l = 5 - 15 μm

w = 200 nm

t = 100 nm

ω r

/2π ∼ 1 MHz

m eff

∼ 10 -16 kg

Q ∼ 10 3 –10 5

Co ferromagnet (single magnetic domain)

• nanometer-sized magnet (single domain)

• magnetization along long axis

(form anisotropy)

• dipole field with strong gradient

B

y

AFM

S

m

N

MFM


Magnetic coupling mechanism

P. Treutlein et al., PRL 99, 140403 (2007).

BEC trapped close

to resonator tip

Resonator oscillations

Si

(atomic spin)

oscillating B-field

couples to atomic spin

Co

F = 2

oscillating field due to cantilever motion:

coupling Hamiltonian:

where

F = 1

m F

= -2 -1 0 1 2


Chip layout ong>andong> trapping potential

simulation of potential

(includes magnetic potential, gravity, ong>andong>

Casimir-Polder surface potential)

coupling:

but: static magnetic field gradient of

Co magnet distorts the trap

(trap frequency cannot be increased

because of collisional loss)

want large G m

compensation magnets to

reduce static field

(oscillatory field unaffected)


A mechanical cavity QED system

Tavis-Cummings model:

N atoms

coupling

single resonator mode

|S,m S

=S>

a+ a

|S,m S

=-S>

S + S - P. Treutlein et al., PRL 99, 140403 (2007).

...

n = 2

n = 1

n = 0

• Atoms (BEC) treated as collective spin S, hS z i = (N 1 -N 0 )/2 (both states trapped)


A mechanical cavity QED system

Tavis-Cummings model:

P. Treutlein et al., PRL 99, 140403 (2007).

N atoms

coupling

single resonator mode

|S,m S

=S>

|S,m S

=-S>

S + S -

a+

a

...

n = 2

n = 1

n = 0

• Atoms (BEC) treated as collective spin S, hS z i = (N 1 -N 0 )/2 (both states trapped)

• cavity QED parameters: g coupling strength

κ = ω r /2Q resonator damping rate (assume Q=10 5 )

γ atom loss rate (surface, three body collisions, ...)

coupling to single atom:

coupling to BEC (N=10 4 ):

(g, κ, γ) = 2π × (62, 14, 0.3) Hz, 250 kHz trap frequency

(gN 1/2 , κ, γ) = 2π × (20, 5, 10) Hz, 3 kHz trap frequency

(limited by collisional loss)


Cooling the cantilever with the atoms

N À hni th

|S| = N/2 ~ 10 4 T = 50 mK: hni th ∼ 10 3

p(n)

S

hni th

n

p(n)

(π-pulse)

S

hni < hni th

n

more possibilities:

•cantilever readout

• driving the cantilever with atoms

• transfer of nonclassical states of the atoms to the cantilever


Outlook: chip prototype

Atom chip prototype

BEC

Co nanomagnet

Si cantilever

gold wires for BEC trapping

fabrication challenges:

• fabricate magnets on free-stong>andong>ing

mechanical structures

• many steps of electron beam lithography


Group members

www.munichatomchip.de

Philipp

Treutlein

Pascal

Böhi

David

Hunger

Johannes

Hoffrogge

Max

Riedel

Stephan

Camerer

Daniel König

(Kotthaus group)

T. W. Hänsch group MPQ ong>andong> LMU Munich

Collaborations:

D. König ong>andong> J. Kotthaus (CeNS, LMU Munich),

J. Reichel (LKB, ENS Paris), M. Wallquist ong>andong> P. Zoller (Innsbruck)

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