ICOLS, Berkeley, June 2013

Christian Roos IQOQI Innsbruck, Austria

Schrödinger cat state spectroscopy

with trapped ions

Joint work with:

C. Hempel, B. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt

Quantum information processing with trapped ions

40Ca+

Outline of talk

How efficiently can we detect a single photon scattering process?

Quantum logic spectroscopy with a two-species ion crystal

Trapped-ion experiments

• Quantum gates by geometric phases

• Geometric phases for spectroscopy with Schrödinger cat states

Qubit manipulation and measurement

P1/2

S1/2

D5/2

40Ca+

Quantum

bit Quantum state

detection 729 nm Quantum state

manipulation

Experimental sequence

1. Initialization in a pure quantum state

3. Quantum state measurement

by fluorescence detection

2. Quantum state manipulation on

S1/2 – D5/2 transition

P1/2 D5/2

t =1s

S1/2

40Ca+

P1/2

S1/2

D5/2 P1/2

S1/2

D5/2

Quantum state

manipulation

P1/2

S1/2

D5/2

Fluorescence

detection

50 experiments / s

Repeat experiments 100 - 1000 times

1-10 ms

0.01- 10 ms

0.2- 3 ms

2- 20 s

5µm

Spatially resolved

detection with

CCD camera:

Two ions:

…

qubit-motion coupling Red sideband

qubit manipulation

…

Trapped-ion laser interactions

Carrier excitation

Blue sideband

Bichromatic excitation

State-dependent forces coupling qubit + motion

Creation of Schrödinger cat states

…

One ion

Two ions:

A. Sørensen, K. Mølmer,

Phys. Rev. Lett. 82, 1971 (1999)

…

Bichromatic excitation

State-dependent forces for entangling gates

Transport in phase space:

Geometric phase gate

The phase F depends nonlinearly on the internal states of the ions

Geometric gates for spin-spin interactions

B. Lanyon et al., Science 334, 57 (2011)

Coupling to further modes:

Building magnetic interactions

from gates by Trotter technique:

(C. Monroe's talk)

Schätz group, MPQ (2008)

Entanglement for quantum-enhanced metrology

Entanglement can enhance spectroscopic measurements with trapped ions:

1. Better signal-to-noise ratio

2. Longer coherence times

3. Quantum logic spectroscopy

Enhanced read-out by quantum logic

state

preparation detection

…

…

non-local

detection

Enta

ngle

r

Spectroscopy decoherence-free subspaces

C. Roos et al., Nature 443, 316 (2006)

N

P. O. Schmidt et al., Science 309, 749 (2005)

J. J. Bollinger et al., PRA 54, R4649 (1996)

D. Leibfried et al., Science 304, 1476 (2004)

Quantum logic spectroscopy

40Ca+ 4Ca+

Creation of correlated quantum states:

Logic ion : cooling + state manipulation + detection

Spectroscopy ion : object to be investigated

spectroscopy

ion logic

ion

Quantum logic spectroscopy:

Detection

Quantum logic spectroscopy

Trapped ions

… that can be laser-cooled

Al

Be

Mg

Sr

Yb

Ca

Hg

Th

Cd

Ba

Ra

In

Th

Ba

Ra

He

Ti

Fe

U

• Optical clocks

• Tests of QED

• Atomic parity violation

• Nuclear isomeric transitions

• Astrophysics

• …

• Molecular ions

Applications:

Cr

… of spectroscopic interest

Trapped ions

… that can be laser-cooled

Al

Be

Mg

Sr

Yb

Ca

Hg

Th

Cd

Ba

Ra

In

Th

Ba

Ra

He

Ti

Fe

U

• Optical clocks

• Tests of QED

• Atomic parity violation

• Nuclear isomeric transitions

• Astrophysics

• …

• Molecular ions

Applications:

Al+ ion Be+ ion

Al+ optical clock (NIST, Wineland group)

Detection of photon absorption on

long-lived transition

Cr

… of spectroscopic interest

Al+ clock:

Spectroscopy ion Logic ion

27Al+

1S0 – 3P0 transition:

9Be+

• great "clock ion"

• hard to detect

• easy to laser-cool

• easy to manipulate

Wineland

group

• easy to detect

Al+ clock:

state mapping by sideband excitation

…

qubit-motion coupling:

Spectroscopy ion

Spectroscopy ion Logic ion

Logic ion

27Al+ 9Be+

Wineland

group

What to do if the upper state is short-lived?

Spectroscopy ion

Detection of photon scattering processes

Absorption measurements

Fluorescence

detection

Detection of photon scattering processes

Momentum transfer from

the light field to the atom

Photon recoil:

Photon detection:

via read-out of logic ion

Scattering ion:

coupling to vibrational mode

Atomic recoil by photon scattering

Photon scattering displaces the motional state In phase space:

(Lamb-Dicke limit)

Atomic recoil by photon scattering

…

Logic ion

Detection with ground-state cooled ion crystal In phase space:

Detection probability for a ground-state cooled ion:

Geometric phases for atomic recoil detection

In phase space:

Geometric phase

by photon scattering

Geometric phase by

cyclic quantum evolution:

Photon recoil detection by

geometric phases + Schrödinger cat states

The photon recoil can modify the path taken in phase space.

The geometric phase carries spectroscopic information.

Use of cat states for turning the global phase into a relative phase

Strategy:

Schrödinger cat state spectroscopy

1. Create a cat state

Protocol:

2. Scatter a photon

3. Recombine cat state

4. Read out qubit

Qubit rotation by scattered photon

Q. A. Turchette et al., PRA 62, 053807 (2000)

W. J. Munro et al., PRA 66, 023819 (2002)

Detecting scattering by qubit measurements

z

y

-1

-1 +1

+1

Bloch

sphere

Qubit rotation by photon scattering

Remarks:

• Photon emission time determines

momentum kick direction

• signal scales with size of the cat

synchronize laser pulse with cat state phase for maximum signal

Photon absorption and reemission

Photon absorption recoil:

Photon absorption + emission recoil

Momentum

space

axial

transverse

0

random emission direction

~61% Maximum detection probability:

Cat state creation by state-dependent force

Time (ms)

Excitation

due to laser pulse shaping

p

q

p

q

p

q

Cat state creation by state-dependent force

p

q

p

q

p

q

Cat state size: Blue sideband oscillations

…

Time(ms)

Excitation

E

xcitation

time

cat pump out analyze

Creation and recombination of a Schrödinger cat state

pulse length (ms)

Excitation

phonons: 0 44 12 150?

cat recombination

How well do we come back to the

original state as a function of cat size?

Mixed crystals: 44Ca+ 40Ca+

Goal: Detect a single scattering event: D3/2 S1/2

Pump out D3/2 Experiment:

Use of amplitude-modulated 866nm laser

producing a pulse train:

pulse separation = oscillation period

P1/2

866 nm

S1/2

D3/2

397 nm

44Ca+

Spectroscopy ion Logic ion

Experimental sequence

time 44Ca+

40Ca+

pump to D

cat cat -1

prepare detect scatter

= Phase of pulse train with respect to phase of cat state oscillation

Schrödinger cat state spectroscopy: Results

• Single-photon detection probability : 12%

• Signal scales with cat state size (currently ~ 8 phonons)

Spectroscopy in a mixed two-ion crystal

C. Hempel et al., arXiv:1304.3270, to appear in Nature Photonics (2013)

Experimental imperfections

Our enemies:

1. Motional heating

2. Motional frequency instabilities

3. Imperfections in spin-motion coupling

What prevents us from increasing the signal by

creating larger cats?

1. Random geometrical phases by motional heating

Random electric fields lead to a displacement

in phase space.

Motional heating:

Rh : heating rate

Cat state spectroscopy:

Coherence after recombining the Schrödinger cat

measured contrast 81%

measured contrast 43%

Heating rate-induced

contrast reduction if

Heating rate improvements

Current trap New trap

~ 2 phonons/s @ 1MHz ~ 40 phonons/s @ 1MHz

Other techniques: optical dipole forces

Gate-based spectroscopy

PRL 107, 243902(2011)

Summary + conclusions

• Not restricted to narrow transitions • Wide range of probe light wavelength • Works without ground state cooling

Cat state quantum logic spectroscopy of ions

Photon detection probability ≈ 12 %

limited by motional heating

Future work: dipole forces instead of spontaneous emission