Quantum measurement and simulation with …...1 Quantum measurement and simulation with Rydberg atoms J.M. Raimond Université Pierre et Marie Curie LKB, Collège de France, ENS, CNRS,

1

Quantum measurement and simulation

with Rydberg atoms

J.M. Raimond

Université Pierre et Marie Curie

LKB, Collège de France, ENS, CNRS, UPMC

RYSQ

Quantum metrology and quantum simulation

• Two important directions in quantum information science.

– Quantum metrology

• How to harness quantum properties to improve the precision of

measurements ?

– Quantum simulation

• How to use a fully controllable and measurable quantum system to

emulate the dynamics of a less accessible but important one ?

• This talk:

– Quantum metrology and quantum simulation with Rydberg atoms

2

Quantum sensing

3

Quantum sensors exploit the strong sensitivity of quantum systems:

to their environment

NV-centers

Dolde et al. PRL 112,

097603 (2014)

Balasubramanian et al

Nat. Mater. 8, 383-38

7 (2009)

Vamivakas et al, PRL 107,

166802 (2011)

Quantum dots

Bunch et al, Science 315,

490-493 (2007)

Electromechanical

resonatorLu et al, Nature 423,

422-425 (2003)

Devoret et al. Nature

406, 1039-1046 (2000)

Single electron

transistorBaumgart et al. PRL 116,

240801 (2016)

Ions

Rydberg atoms

Sedlacek et al.

Nat. Phys. 8, 819–824

(2012)

Quantum-enabled sensing

• Use entanglement and/or non-classical states to improve sensitivity

4

Estimation of physical quantity A

Evolution Measure-

ment

AEstimation

Precision depends on initial

state of the meter:

Best precision:

semi-classical states:

Standard Quantum Limit

non-classical states:

Heisenberg Limit

Example: Large spin J

Measure rotation angle

with semi-classical

state:

“spin coherent state”

SQL: intrinsic

fluctuations of direction

1/√J

Measure rotation angle with non-classical state:

squeezed state[1] or Schrödinger cat state

[1]JG Bohnet et al. Nature Photonics 8, 731–736 (2014) [1]O Hosten et al. Nature 529, 505-508 (2016)

1/J

Quantum simulation

5

• An insight into the properties of complex many-body systems

– Realize a fully controllable/measurable system with the same

dynamics as the system of interest

– More efficient than exact classical computations for large Hilbert

spaces (full dynamics of 42 spins out of reach of classical machines)

• Main requirements

– High-quality individual quantum systems

– Tailorable interactions between them

– Scalable methods for1D-2D-3D arrangements and for initialization

– Complete final quantum state read-out

– Possibility to introduce a tailorable, reproducible disorder.

• Realization a priori simpler than that of a full-fledged quantum

computer

• One of the most promising outcomes of quantum information science

– A very active field worldwide

Quantum simulation

• Many realizations already

6

Trapped ions in 1D

Martinez et al. Nature 534 516

Superconducting circuits Barends et al. Nature 534,222

Atomic lattices Zeiher et al. Nat. Phys. 12,1095

Rydberg atoms

Barredo et al. PRL 114 113002

Trapped ions in 2D

Bohnet et al., Science 352 1297And many more…

This talk

• Quantum-enabled electrometer and magnetometer

– Huge polarizabilities and coherent manipulations of Rydberg manifold

• Highly sensitive

• Measures non-trivial statistical properties of the field

– Huge magnetic moment of circular states and cat-states made up of

circular states

• A quantum-enabled magnetometer

• Towards a circular state quantum simulator

• Spontaneous-emission-protected circular state with extremely long

lifetimes.

• Trapped in an optical lattice

– A simulator for a general nearest-neighbor spin array Hamiltonian

7

Quantum-enabled electrometer and magnetometer

8

Rydberg atoms

• Very excited atomic states blessed with remarkable properties

– Long lifetimes

• 100 µs for low-l states in the n=50 manifold

• 30 ms for circular states

– Huge dipole matrix elements

• Highly coupled to microwave fields

• Very sensitive to external electric fields

• Huge dipole-dipole interaction

– Rich level structure

9

Rydberg states level structure

• A large range of field sensitivities

– Ramsey spectroscopy on large polarizability states to measure F

• Electrometer at the Standard Quantum Limit

– Cat-like superpositions of high- and low-polarizability states

• Quantum electrometer beyond SQL

– Superposition of circular states with opposite m values

• Quantum-enabled magnetometer10

Circular state

Large positive polarizability

Large negative polarizability

Circular state

Our quantum stage

• Stark levels of hydrogen

m=0 m=1 . . . . . .

. . . . . . .

. . .

. . . .

51C

m=2 m=n-1

100 MHz in 1 V/cm for n=51

A spin ladder in the Rydberg manifold

• Evolution with resonant s+ rf excitation

– Isolate a J=25 angular momentum closed system

• with 51 equidistant levels

– (within the second order Stark effect and quantum defects

corrections)

51C

m=n-1m=0 m=1 . . . . . .

. . . .

m=2

A very simple experimental set-up

Atomic beam

Laser

Laser

r.f. electrodes

for radiating

s+ RF field

at 230 MHz

Field-

ionization

detector

F

A. Facon et al., Nature, 535, 262 (2016)

The Bloch sphere and the spin coherent states (SCS)

• Rabi rotation of the spin driven by a s+-polarized rf field

– the spin is in a spin coherent state (SCS) rotating on the sphere

Y

Z

X

A simple experiment

• Rabi rotation of the spin in a resonant rf field

15A. Signoles et al. PRL, 118 253603

A simple experiment

• Rabi rotation of the spin in a resonant rf field

16

More than 20 coherent Rabi rotations between a laser-

accessible low-l state and the circular state

An excellent theoretical understanding

A possible interface between optical and

microwave photons

Promising level of control in the complex hydrogenic

manifold

A. Signoles et al. PRL, 118 253603

Electric field measurement by Ramsey spectroscopy

• Ramsey sequence

rf p/2 <pulse rf p/2 pulse

with phase fR

Free precession

f(T)= ws.T

Standard Quantum Limit (SQL)

Two fields separated by DF=566 µV/cm


51C

Interrogation time

f f

Quantum enabled measurement

• Measure the total phase F accumulated by the spin in state 50 (g)

– Needs a phase reference

• Circular state 51 (e)

– Not affected by rf rotations in

50 manifold

• A double Ramsey scheme

• An intermediate spin cat state.

18

A. Facon et al., ArXiV 1602.02488 and Nature, 535, 262 (2016)

Quantum enabled measurement

• Measure the total phase F accumulated by the spin in state 50 (g)

– Needs a phase reference

• Circular state 51 (e)

– Not affected by rf rotations in

50 manifold

• A double Ramsey scheme

• An intermediate spin cat state.

19


Interrogation time

Beyond the SQL

• Scanning the radiofrequency phase

– Two fields separated by DF=566 µV/cm around F0=5.50527 (21) V/cm

– Clear gain in sensitivity to the field

20


Beyond the SQL

• Scanning the microwave phase

– Two fields separated by DF=566 µV/cm around F0=5.50527 (21) V/cm

21


Gain in sensitivity to the field


Electric field measurement sensitivity

Single-shot electric field measurement standard deviation

s F

1


E.K. Dietsche, In preparation

200 µV/cm !

A promising electrometer

• Achieved sensitivity

– 200 µV/cm for 200 ns interrogation time

• A single electron at a 200 µm distance!

– Competes with the best electrometer devices

• Assets

– non-invasive

– Space- and time-resolved

• Few µm cold atom samples

• MHz detection bandwidth

• Possible practical applications for characterization of mesoscopic devices

»

23

Towards detecting a single electron

in a Carbone nanotube quantum

dot !

• Interferometry with positive and negative polarizability statestim

e

t-t+

51C

49C

An AC quantum-enabled electrometer

24

Total Ramsey phase a [F(t+)-F(t-)]

Electric field noise measurement

• Differential fringes in a stochastic field

25

with

Electric field fluctuations:

C0 C0Cr

Contrast reduction

Contrast directly measures the noise time correlation function

Uncorrelated noise measurement

26

t+ t-T = 9µs = t++T

Digitally generated

noise with 1.5 µs

correlation

-0,02 -0,01 0,00 0,01 0,020,0

0,2

0,4

0,6

0,8

1,0 B

0054 19,71Vpp

0055 15Vpp Up

0056 10Vpp Up

0057 5Vpp Up

ErreurU

Fit Curve of 0054 Up

Fit Curve of 0055 15Vpp Up



Fit Curve of 0058 0 Vpp UpPro

ba

bili

ty

nmw

(MHz)

0 10 20 30 40 500,0

0,2

0,4

0,6

0,8

1,0Plot Fit multiple des ups [54-58]

1

2

3

4

5

S1x2

ex2

Co

ntr

ast

sF (mV/m)

Second order

Exact

C0

• Contrast of Ramsey fringes versus T=t--t+

– A direct measurement of the noise correlation

• And hence of the field fluctuations spectrum

Electric noise correlation function

No noise

1.5 µs correlation

0.5 µs correlation

White noise

E.K. Dietsche, in preparation

T

σF = 36mV/m

Quantum-enabled magnetometry

Stark energy levels

circular

state

@ F=234.5V/m

circular

state

• Cat-like superposition of ‘opposite’ circular states

• Large Δm very sensitive to magnetic field

• Same polarizability insensitive to electric field

Preparation of opposite circular states

circular

state

circular

state

|+52c⟩︎

|-50c⟩︎

initial

state

|+52,m=2⟩︎

Stark levels:

Pulse

sequence:𝜏

tprep~2µs trec~2µs

Ramsey fringes

-0,02 -0,01 -0,00 0,01 0,020,0

0,2

0,4

0,6

0,8

1,0

Model Sine

Equation y=y0+A*sin(pi*(x-xc)/w)

Plot 0227 -40 mV 0226 -20 mV 0223 0mV 0228 0mV 0224 10mV 0225 30mV

y0 0,25761 ± 0,0017 0,25679 ± 0,00156 0,2558 ± 0,00173 0,2524 ± 0,00169 0,253 ± 0,00173 0,2559 ± 0,00161

xc -0,06233 ± 4,533 -0,05086 ± 5,0579 -0,03805 ± 5,9707 -0,03776 ± 5,9215 -0,06657 ± 4,3012 -0,07664 ± 4,6818

w* 0,0113 ± 1,35973 0,0113 ± 1,35973 0,0113 ± 1,35973 0,0113 ± 1,35973 0,0113 ± 1,35973 0,0113 ± 1,35973

A 0,17362 ± 0,0022 0,16935 ± 0,00204 0,1716 ± 0,00223 0,1693 ± 0,0022 0,1733 ± 0,00219 0,17241 ± 0,00209

Reduced Chi- 1,07168

R-Square(CO 0,99722 0,99802 0,99649 0,99738 0,99667 0,99734

R-Square(CO 0,99725

Adj. R-Square* 0,99679

0223 0mV

0227 -40 mV

Fit Curve of 0223 0mV

Fit Curve of 0227 -40 mV

Pro

ba

bili

ty

nmw

(MHz)

-0,05 -0,03 -0,01 0,01 0,03 0,050,0

0,2

0,4

0,6

0,8

1,0

Model Sine

Equation y=y0+A*sin(pi*(x-xc)/w)

Plot 0237 -100 mV 0235 -80 mV 0234 -40mV 0231 0mV 0236 0mV 0232 20mV 0233 60mV 0238 100 mV

y0 0,25738 ± 0,00172 0,25824 ± 0,00172 0,25742 ± 0,00172 0,25571 ± 0,00162 0,25803 ± 0,00161 0,25619 ± 0,00168 0,25728 ± 0,00173 0,25467 ± 0,00171

xc -0,0899 ± 1,16149E- -0,10044 ± 1,20014E -0,06536 ± 1,14792E -0,08249 ± 1,07269E -0,08432 ± 1,06912E -0,08952 ± 1,11199E -0,05809 ± 1,1357E- -0,07596 ± 1,1502E-

w* 0,02638 ± 3,67815E 0,02638 ± 3,67815E- 0,02638 ± 3,67815E- 0,02638 ± 3,67815E- 0,02638 ± 3,67815E- 0,02638 ± 3,67815E- 0,02638 ± 3,67815E 0,02638 ± 3,67815E

A 0,16216 ± 0,00226 0,1655 ± 0,00226 0,16283 ± 0,00226 0,16494 ± 0,00211 0,16263 ± 0,00211 0,16401 ± 0,00219 0,16534 ± 0,00225 0,16115 ± 0,00226

Reduced Chi-Sq 1,15258

R-Square(COD) 0,9991 0,99745 0,99827 0,99574 0,99607 0,99669 0,99653 0,99451

R-Square(COD)* 0,99676

Adj. R-Square* 0,99622

Fit Curve of 0231 0mV

Fit Curve of 0234 -40mV

0231 0mV

0234 -40mV

Pro

ba

bili

ty

nmw

(MHz)

𝜏 = 7.2µs

𝜏 = 20µs

• B = 0 µG

o B = -324 µG

• B = 0 µG

o B = -324 µG

𝜏tprep~2µs trec~2µs

-500 0 500-4

-2

0

2

4

6

8

10

19,942

Phase

Phase

Linear Fit of Sheet1 K"Phase"

Linear Fit of Sheet1 J"Phase"

F (

rad

)

B (µG)

Equation y = a + b*x

Plot Phase

Weight Instrumental

Intercept 1,82625 ± 0,05033

Slope -0,14734 ± 0,00466

Residual Sum of Squares 7501,92039

Pearson's r -0,998

R-Square(COD) 0,99601

Adj. R-Square 0,99501

Equation y = a + b*x

Plot Phase

Weight Instrumental

Intercept 2,71724 ± 0,08791

Slope -0,05532 ± 0,00158

Residual Sum of Squares 9728,5196

Pearson's r -0,99757

R-Square(COD) 0,99514

Adj. R-Square 0,99433

7,237

Comparison to SQL & HL

SQL HL

~3.5-times (-10.8dB) below the SQL

for 𝜏 = 20µs:

Single atom sensitivity

Observed sensitivity 400pT/√Hz

Can be improved by a factor 100 with slow atoms taking benefit of the

circular states lifetime: 4pT/√Hz within reach

Well beyond other single-atom sensors

Towards a circular state quantum simulator

32

Dipole-Dipole interaction between Rydberg atoms

• A long range, strong interaction

– Early evidence J.M. Raimond, et al J. Phys. B 14, L655 (1981)

– Direct measurement Béguin et al PRL 110, 263201

– Two 60S Rydberg levels

• Isotropic, repulsive interaction

• For distances > 3 µm

• Order of magnitude

– 8.8 MHz at 5 µm

– To be compared with a typical 20 kHz kinetic energy in cold

cloud at 1 µK

33

𝒓

Dipole blockade and facilitation

• Laser excitation of a dense cloud

of ground state atoms

– At resonance:

• blockade radius

determined by the

excitation linewidth

– Above resonance (positive

laser detuning)

• Faciliation radius

Excitation of atomic

clusters

34

RB

ȁ ۧ𝑔, 𝑔

𝑟

ȁ ۧ𝑔, 𝑅 , ȁ ۧ𝑅, 𝑔

ȁ ۧ𝑅, 𝑅

𝐸

Rbl

D

Rf

Rf

Γ, Ω

ȁ ۧ𝑔, 𝑔

𝑟

ȁ ۧ𝑔, 𝑅 , ȁ ۧ𝑅, 𝑔

ȁ ۧ𝑅, 𝑅

𝐸

M. Lukin et al. Phys. Rev. Lett. 87, 037901

T.M. Weber et al. Nat. Phys. 11, 157

Quantum simulation with Rydberg atoms

• Rydberg atoms ideal for many-body physics simulation

– Strong interactions

– Easy detection

• Two limitations

– Finite lifetime (100 µs for laser accessible states)

• And blackbody-induced transfers

– Atomic motion

• An even more severe limitation to the useful time

– Reduced but not cancelled by Rydberg dressing of ground states

• Is it possible to operate with long-lived Rydberg atoms trapped in an

optical lattice?

– Towards a trapped circular Rydberg atom quantum simulator

• A linear chain of interacting circular atoms at a few µm distance

• Possible extensions to higher dimensions.

35

T.L. Nguyen et al, arXiv:1707.04397

E. A. Goldschmidt, Phys. Rev. Lett. 116, 113001

https://arxiv.org/abs/1707.04397

D

a

F

• Non-degenerate with manifold in F and B fields

• Long lifetime

– 25 ms for 48C. Main decay channel: microwave spontaneous emission

on a s+ transition

• Spontaneous emission inhibition

– Emission inhibited in a capacitor below cut-off.

• 2500 s life in a 13 x 2 mm capacitor !

– Remaining decay channels

• vdW interaction state mixing

• Blackbody absorption (0.5 K)

• Lifetime 60 s

– Very long lifetime for a pair of interacting 48C atoms at a 5 µm

distance

• Trapping mandatory

Circular Rydberg atoms

36

D. Kleppner Phys. Rev. Lett. 47, 233 (1981)

D

a

F

Non• -degenerate with manifold in F and B fields

Long lifetime •

25 – ms for 48C. Main decay channel: microwave spontaneous emission

on a s+ transition

Spontaneous emission inhibition•

Emission inhibited in a capacitor below cut– -off.

2500 • s life in a 13 x 2 mm capacitor !

Remaining decay channels–

vdW• interaction state mixing

Blackbody absorption (• 0.5 K)

Lifetime • 60 s

Very long lifetime for a pair of interacting – 48C atoms at a 5 µm

distance

Trapping mandatory•

Circular Rydberg atoms

37

D. Kleppner Phys. Rev. Lett. 47, 233 (1981)

Circular states laser trapping

• Circular states can be laser-trapped !

– Ponderomotive electron energy:

• atoms are low-field seekers

• a large trap

– ~10 times greater polarizability that of ground state Rubidium

at 1 µm wavelength

– Trapping almost independent of principal quantum number

• Low trap-induced decoherence

– Impervious to photoionization

• severe limitation for low l states Saffman et al. Phys. Rev. A 72, 022347

• Long term trapping

– 50 s lifetime taking into account Compton scattering and realistic

vacuum conditions in a cryogenic environment

– >1 s lifetime for a 40 atoms chain

38

S. K. Dutta et al. Phys. Rev. Lett. 85, 5551

A simple trap geometry for a 1-D lattice

• Trapping lasers at 1 µm

– LG mode along Ox (transverse trap)

– Two Gaussian beams at a small angle

• Longitudinal lattice with an adjustable spacing

– d= 5 to 7 µm

– 24 kHz longitudinal oscillation frequency

39

Circular Rydberg interaction

• Choice of levels

– Encode spin states on 48C and 50C

• A repulsive van der Waal interaction (a 1/d6) between atoms in the

same levels at a distance d

• A second order spin exchange interaction (48C,50C to 50C, 48C)

(a 1/d6)

• Dress the atomic transition with a near-resonant microwave

– Rabi pulsation W, detuning D

• Makes the ground state nontrivial

• Can be fed in the capacitor in an evanescent mode

• Realization of the XXZ spin-1/2 chain Hamiltonian

40


An XXZ spin Hamiltonian•

– J= 17 kHz for d= 5 µm, J= 2.3 kHz for d=7 µm

Spin– exchange time 1/4J in the 15-100 µs range

Trapping time for a – 40 atoms chain is 104 exchange times!

All parameters under control•

– D and W through dresssing microwave source

– Jz through electric and magnetic fields

All can be changed and modulated over time scales much shorter •

than 1/4J

41


• An XXZ spin Hamiltonian

– J= 17 kHz for d= 5 µm, J= 2.3 kHz for d=7 µm

– Spin exchange time 1/4J in the 15-100 µs range

– Trapping time for a 40 atoms chain is 104 exchange times!

• All parameters under control

– D and W through dresssing microwave source

– Jz through electric and magnetic fields

• All can be changed and modulated over time scales much shorter

than 1/4J

42

B=13 Gauss

B=14 Gauss

B=15 Gauss

A rich phase diagram

• Within reach of parameters tuning range

– D=0Dimitriev et al, JETP 95 538

• For realistic atom numbers (MPS for 40 atoms)

43

Deterministic chain preparation

Van der Waals evaporation•

LG and `plug– ’ beams trap

One weak, one strong•

Load ~ – 100 circular atoms

Compress the trap. Atom evaporate above weak plug–

Classical – modelization

Final atom determined by trap length•

Deterministic chain preparation up to ~– 40

Effective cooling•

Final motion amplitude close to ground state one–

Chain state detection•

Interrupt exchange (– 48C to 46C, exchange stops)

Resume evaporation, routing atoms one by one to a field– -ionization

detector: measure all sz observables

Additional hard microwave pulse: measure all spin observables.–44

Deterministic chain preparation

• Van der Waals evaporation

– LG and `plug’ beams trap

• One weak, one strong

– Load ~ 100 circular atoms

– Compress the trap. Atom evaporate above weak plug

– Classical modelization

• Final atom determined by trap length

– Deterministic chain preparation up to ~40

• Effective cooling

– Final motion amplitude close to ground state one

• Chain state detection

– Interrupt exchange (48C to 46C, exchange stops)

– Resume evaporation, routing atoms one by one to a field-ionization

detector: measure all sz observables

– Additional hard microwave pulse: measure all spin observables.45

Perspectives

• Adiabatic exploration of the phase diagram

– Encouraging simulations for 14 atoms including residual atomic

motion

• Departures from adiabaticity

– Defects creation, Kibble Zurek mechanism

• Adding disorder with a speckle field

– Bose glass physics

– Random singlet phases (nontrivial long-range correlations)

• Ladder geometry and Haldane physics

– Bringing two chains together

• Antiferromagnetic coupling between ferromagnetic chains

• Maps onto Haldane physics

– Edge states and topological order

• Fast variations of Hamiltonian

– Quenches, Excitation spectroscopy, Floquet engineering

• A bright future for a circular state simulator.

– Let us build it! Laser trapping of a circular atom in progress46

47

S. • Haroche, M. Brune,

J.M. Raimond, S. Gleyzes, I. Dotsenko,

C. Sayrin

Cavity QED•

V. – Métillon, D. Grosso, F. Assémat

QZD and metrology•

A. – Signoles, A. Facon,

E.K. – Dietsche, A. Larrouy

• Circular state simulator

Thanh– Long Nguyen, T. Cantat-Moltrecht

R. – Cortinas, B. Navon

Spin chain theory•

Th. – Jolicoeur, G. Roux (LPTMS, Orsay)

€€:• EC (RYSQ), ANR (TRYAQS),CNRS, UMPC, ENS, CdF

A team work

www.cqed.org

Documents

Quantum measurement and simulation with …...1 Quantum measurement and simulation with Rydberg atoms J.M. Raimond Université Pierre et Marie Curie LKB, Collège de France, ENS, CNRS,