QUEST - Centre for Quantum Engineering and Space-Time Research

Single mode squeezing for Interferometry beyond shot noise

Bernd Lücke

J. Peise, M. Scherer, J. Kruse, O. Topic, W. Ertmer, C. KlemptInstitute of Quantum Optics, Leibniz Universität Hannover, Germany

G. Gebreyesus, F. Deuretzbacher, L. SantosInstitute of Theoretical Physics , Leibniz Universität Hannover, Germany

J. ArltQUANTOP, Institut for Fysik og Astronomi, Aarhus Universitet, Denmark

P. Hyllus, A. SmerziINO-CNR BEC Center and Dipartimento di Fisica, Universita‘ di Trento, Italy

L. PezzeLaboratoire Charles Fabry, Institut d’Optique, 91127 Palaiseau, France

QUEST - Centre for Quantum Engineering and Space-Time Research

A typical interferometer

Counter

| α >

θ

θest

| 0 >

N-1

N+1

π 2π 3πθ

< N

+1 -

N-1 >

S

θest2

QUEST - Centre for Quantum Engineering and Space-Time Research

The origin of shot noise

-5 -3 -1 +1 +3 +5

coun

ts

7

6

5

4

3

2

1

N+1 - N-1

3

QUEST - Centre for Quantum Engineering and Space-Time Research

The origin of shot noise

+1

+1

+1

-1

+1

+3

coun

ts

7

6

5

4

3

2

1

N+1 - N-1

-5 -3 -1 +1 +3 +5

4

QUEST - Centre for Quantum Engineering and Space-Time Research

The origin of shot noise

coun

ts

7

6

5

4

3

2

1

-1

-1

+1

-1

+1

-1 N+1 - N-1

-5 -3 -1 +1 +3 +5

5

QUEST - Centre for Quantum Engineering and Space-Time Research

The origin of shot noise

coun

ts

7

6

5

4

3

2

1

N

N+1 - N-1

-5 -3 -1 +1 +3 +5

6

QUEST - Centre for Quantum Engineering and Space-Time Research

Shot noise limited sensitivity

π 2π 3π

θ

< N

+1 -

N-1 >

NNN

SS

est1

/

S

θest

7

QUEST - Centre for Quantum Engineering and Space-Time Research

How can you beat this limit?

uncorrelated particles

shot-noise limit

entangled particles

Heisenberg limitNest1

Nest1

8

QUEST - Centre for Quantum Engineering and Space-Time Research

Twin-Fock interferometer

Introduction

outline

N| N||

Fock state interferometerN| N||

9

QUEST - Centre for Quantum Engineering and Space-Time Research

Spin dynamics as a source of entanglement

mF: -1 0 +1

2nd quantization 1st quantization

1,1|| ,|,|~|

10

QUEST - Centre for Quantum Engineering and Space-Time Research

Measuring sub shot-noise fluctuations

shot noise

detection noise

total number of atoms

stan

dard

dev

iatio

n/2

• 7dB below shot noise @ 8000 atoms• detection noise σ(Jz) = 20 atoms

11

QUEST - Centre for Quantum Engineering and Space-Time Research

σJz

ΦJz= (N-1 - N+1)/2

σΦ

Jx

Jy

Representation on the generalized Bloch sphere

RF

Entangled Twin-Fock stateproduced using spin dynamics

12

coherent superpositionproduced using rf preparation

Jz

Jx

Jy

σJz=0

QUEST - Centre for Quantum Engineering and Space-Time Research

Uncorrelated input vs. Twin-Fock input

13

QUEST - Centre for Quantum Engineering and Space-Time Research

Output signal

14

QUEST - Centre for Quantum Engineering and Space-Time Research

Sensitivity

15

QUEST - Centre for Quantum Engineering and Space-Time Research

Twin-Fock interferometer

Introduction

outline

N| N||

Fock state interferometerN| N||

16

QUEST - Centre for Quantum Engineering and Space-Time Research

01 NNN total

NN ,|

2,| NN

NnCNn

n ,|||

Counter

| NN total|

N|

CounterN|-1

0

+1

17

QUEST - Centre for Quantum Engineering and Space-Time Research

Does it work with two different Fock states?

NN ,|

2,| NN

Jz = (N

+1 - N-1 )/2

counts

Jz = (N

+1 - N-1 )/2

18

QUEST - Centre for Quantum Engineering and Space-Time Research

Does it work with a coherent and a Fock input state?

Counter

|

N|

11 NNN total

NN total|

NnCNn

n ,|||

NmNn est 2

2

NnnNmest

21

Ultrasensitive Atomic clock with single-mode number-squeezing,L. Pezzé and A. Smerzi, arXiv:1004.5486v1

19

QUEST - Centre for Quantum Engineering and Space-Time Research

Measuring a single output port

Counter

|

N|

coun

ts

N+1N

θ = 0

N+1N

θ<< π

N+1N

Θ = π

|α|²

QUEST - Centre for Quantum Engineering and Space-Time Research

Sub shot-noise sensitivity can be achieved with Twin-Fock states produced by spin dynamics

For sub shot-noise sensitivity entanglement is necessary

summary

N| N||

A single Fock state and an coherent input state are also suitable for sub shot-noise interferometryN| N||

21

QUEST - Centre for Quantum Engineering and Space-Time Research

Thank you for your attention.

22

W.Ertmer I.Geisel C.Klempt J.Peise B.Lücke J.Mahnke S.Coleman

QUEST - Centre for Quantum Engineering and Space-Time Research

Phase estimation for θ=π/2co

unts

Jz = (N+1 - N-1)/2co

unts

Jz = (N+1 - N-1)/2

coherent input state Twin-Fock input state

QUEST - Centre for Quantum Engineering and Space-Time Research

Phase estimation for θ=π/2co

unts

Jz = (N+1 - N-1)/2co

unts

Jz = (N+1 - N-1)/2

coherent input state Twin-Fock input state

QUEST - Centre for Quantum Engineering and Space-Time Research

Phase estimation for θ=π/2co

unts

Jz = (N+1 - N-1)/2co

unts

Jz = (N+1 - N-1)/2

coherent input state Twin-Fock input state

QUEST - Centre for Quantum Engineering and Space-Time Research

Actual measurement

-1 0

6

4

2

0

coherent input state Twin-Fock input state

1(N+1 - N-1)/N

QUEST - Centre for Quantum Engineering and Space-Time Research

Jz

JyJx

The gerneralized Bloch sphere

Multi particle Bloch sphere:

Jx (a† b + a b†)/2 Jy = -i (a† b - a b†)/2 with Jz = (N+1 - N-1)/2 Jz (a† a - b† b)/2

QUEST - Centre for Quantum Engineering and Space-Time Research

Expension of the state reveals its entanglement

NnCNn

n ,|||

Why is this state not entangled?

nmCC nnm

m ,||| ,,

,

2,0|1,1|0,2|2 2,0,1,1,0,2, CCCCCCnm

Because…

In 1st quantization: ||||~|