and nanomechanical resonators on an atom chip

Ultracold atoms coupled to micro- <strong>and</strong>
<strong>nanomechanical</strong> <strong>resonators</strong> 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 <strong>and</strong>
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 micro<strong>and</strong>
nanostructures

Interactions between two very different systems
Bose-Einstein
condensate
Chip-based micro<strong>and</strong>
nanostructures
manipulate
„Quantum laboratory for atoms on a microchip“
• simple path to BEC <strong>and</strong> Fermi degeneracy
• compact clocks <strong>and</strong> 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 micro<strong>and</strong>
nanostructures
probe
„Quantum AFM tip“
• study atom-surface interactions
• microscopy of magnetic, electric, or microwave fields
• monitor dynamics of on-chip mechanical <strong>resonators</strong>,
nanomagnets, Josephson junctions, ...

Interactions between two very different systems
Bose-Einstein
condensate
Chip-based micro<strong>and</strong>
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 <strong>and</strong> decoherence

Outline
Atom chips
• basic concepts
• experimental setup
• BEC preparation
Ultracold atoms near the chip surface
• atom-surface interactions
• coherent manipulation <strong>and</strong>
coherence lifetime
BEC coupled to micro- <strong>and</strong>
<strong>nanomechanical</strong> <strong>resonators</strong>
• 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 <strong>and</strong>
coherence lifetime
BEC coupled to micro- <strong>and</strong>
<strong>nanomechanical</strong> <strong>resonators</strong>
• coupling via surface potential
• magnetic coupling:
a mechanical cavity QED system

Ultracold atoms close to a “hot“ surface
Loss, heating <strong>and</strong> 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
<strong>and</strong>
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 <strong>and</strong>
coherence lifetime
BEC coupled to micro- <strong>and</strong>
<strong>nanomechanical</strong> <strong>resonators</strong>
• coupling via surface potential
• magnetic coupling:
a mechanical cavity QED system

Micro- <strong>and</strong> <strong>nanomechanical</strong> <strong>resonators</strong>
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
<strong>and</strong> mechanical <strong>resonators</strong>
paper system coupling
D. J. Winel<strong>and</strong> 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 <strong>and</strong> 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 <strong>and</strong> trapping potential
simulation of potential
(includes magnetic potential, gravity, <strong>and</strong>
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-st<strong>and</strong>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 <strong>and</strong> LMU Munich
Collaborations:
D. König <strong>and</strong> J. Kotthaus (CeNS, LMU Munich),
J. Reichel (LKB, ENS Paris), M. Wallquist <strong>and</strong> P. Zoller (Innsbruck)