quantum information processing as told by: david g. cory department of nuclear science &...

Quantum Information Processing

as told by: David G. CoryDepartment of Nuclear Science & Engineering

Massachusetts Institute of Technology

Neutron Interferometr

yDmitry PushinDmitry PushinPhysics, MITPhysics, MIT

Dr. Sekhar Ramanathan Dr. Sekhar Ramanathan

Dr. Timothy Havel

Professor Seth Lloyd

Dr. Sergio Valenzuela

Dr. Will Oliver

Dr. John Bernard

Dr. M. Arif, Dr. M. Arif, NISTNIST

University of WaterlooUniversity of WaterlooProfessor Joseph EmersonProfessor Joseph EmersonProfessor Raymond LaflammeProfessor Raymond LaflammeDr. Jonanthan BaughDr. Jonanthan Baugh

Dr. Timothy Havel


Dr. Sekhar Ramanathan Dr. Sekhar Ramanathan Dr. Joseph EmersonDr. Joseph EmersonPaola Cappellaro Michael Henry Jonathan HodgesSuddhasattwa Sinha Jamie Yang

1900 1910 1920 1930

Planck - photons

1940 1950 1960

Bell - locality testsBell - locality tests

Bohr - old QT, interpretation Bohr - old QT, interpretation Dirac - relativistic wave-equationDirac - relativistic wave-equation

EinsteinEinstein

Heisenberg - new QTHeisenberg - new QT

Schrödinger - wave equationSchrödinger - wave equation

Landauer - Landauer - information is physicalinformation is physical

1970 1980

1900 1920 1940 1960 1980 2000 2020

Old QTOld QT New QTNew QT Tests Tests QIPQIP

HarocheHarocheAspectAspect ZeilingerZeilinger

Quantum mechanics permits information processing beyond the classical limit

These new possibilities are

Macroscopic Quantum CoherenceMacroscopic Quantum CoherenceInterferometer

Neutron

Beam

Sample

Phase Shifter

Detectors

H-beam

O-beam

Neutron interferometryNeutron interferometry

an example of macroscopic quantum coherencean example of macroscopic quantum coherence

3-blade, interferometer3-blade, interferometer

Size ~ 10 cmSize ~ 10 cm

NeutronsNeutrons

2.1 Å2.1 Å

~ 1800 m/s~ 1800 m/s

~ 50 µs / 10 cm~ 50 µs / 10 cm

1 neutron every 0.35 s1 neutron every 0.35 s



Bragg scattering Bragg scattering

Each neutron Each neutron

is coherently spread is coherently spread

over two pathsover two paths

€

ψ = 12

upper + lower( )



Ignore the beam Ignore the beam

that is scattered that is scattered

out of the out of the

interferometerinterferometer

No information lost.No information lost.

The transmitted and reflected beams The transmitted and reflected beams

carry the same information,carry the same information,



€

ψ = 12

eiφ upper + lower( )

€

ψ = 12

upper + lower( )

Third blade recombines Third blade recombines

the beams and allows the beams and allows

them to interfere.them to interfere.



€

ψO =12

eiφtrr upper + rrt lower( )t - transmittedt - transmitted

r - reflectedr - reflected

€

ψH =12

eiφtrt upper + rrr lower( )



€

IO = ψO2 = t 2 r 4 1+ cos φ( )[ ]Measure the neutronMeasure the neutron

Intensity.Intensity.

In this case that is the In this case that is the

number of neutronsnumber of neutrons

per unit time.per unit time.

€

IH = ψH2 = r 2 t 4 + r 4

( ) − r 2 t 2 cos φ( )[ ]

Interference

€

re iφ2 ′ k

242

0 trA ψ=

][6242

0 rrtB +=ψ

A:

B:

|path I |path II

€

t e iφ1 k

€

k

C:

€

rre i ˜ φ 2 k

€

rt e i ˜ φ 1 ′ k

D:

3He detectors

H-beam

O-beampath I

path II

ABCD

O-beam:

€

rrte i ˜ φ 1 k + trre i ˜ φ 2 k

H-beam:

€

trte i ˜ φ 1 ′ k + rrre i ˜ φ 2 ′ k

€

IO = rrte i ˜ φ 1 k + trre i ˜ φ 2 k2

= A[1+ cos(Δφ)]

€

IH = trte i ˜ φ 1 ′ k + rrre i ˜ φ 2 ′ k 2

= B − Acos(Δφ)



Clothier et al, (1991) PRA 44, 5357Clothier et al, (1991) PRA 44, 5357

Neu

ton

s/ 3

min

Neu

ton

s/ 3

min

phasephase



A simple exampleA simple example

of probability amplitudes.of probability amplitudes.

Set Set so that I so that IHH=0.=0.

€

IH ∝ 1− cos φ( )[ ]

€

IO ∝ 1+ cos φ( )[ ]

€

IO ∝ 2

€

IO ∝1

€

IO ∝1

€

IH ∝1

Coherent Neutron ImagingCoherent Neutron Imaging

€

ψ phase ⏐ → ⏐ ⏐ ψ0eiλ N (z)bc (z)dz∫

z − path

N(z) - particle density

bc z( ) - coherent scattering length

€

IO ∝ 1+ cos kz( )[ ]

€

wedge - linear phase ramp

φ(z) = λNbcz tan ϑ( )

ϑ - wedge angle

k = λNbc tan ϑ( )

Spatially encoding of the neutron beam

3He detector

position sensitive detector

wedge

Neutron beam

By spatially encoding beam we are introducinga new degree of freedom. By tracing this degree we can:• measure spatial properties of materials (softmatter)• use it as controlled decoherence in QIP

Coherent Neutron ImagingCoherent Neutron Imaging

€

IO k( )∝ 1+ w(z)cos kz( )∫ dz[ ]

€

sample, assume bc is spatially invariant.

φs z( ) = λbcNw(z)

w(z) - sample width

€

wedge - linear phase ramp

φ(z) = λNbcz tan ϑ( )

ϑ - wedge angle

k = λNbc tan ϑ( )

Vary k to collect a complete set of Vary k to collect a complete set of

Fourier components. The resolutionFourier components. The resolution

depends on S/N not the detector.depends on S/N not the detector.

Spatial encoding

- No sample

- Step-like sample

The fit is to the known sample geometry, parameters are step location and size.Notice that each point is 50 minutes of averaging.

Spin Polarized Neutrons

Polarizer

Analyzer

Detector

π

π/2

+ = not

Interference and spin

€

re iφ2 ′ k ↓

242

0 trA ψ=

][6242

0 rrtB +=ψ

A:

B:

|path I |path II

€

t e iφ1 k ↑

€

k ↑

C:

€

rre i ˜ φ 2 k ↓

€

rt e i ˜ φ 1 ′ k ↑

D:

H-beam

O-beam path I

path II

ABCD

O-beam:

€

1

2r( rte i ˜ φ 1 + trre i ˜ φ 2 ) k ↑

H-beam:

€

trte i ˜ φ 1 ′ k ↓ + rrre i ˜ φ 2 ′ k ↑

€

IO = 12 rrte i ˜ φ 1 + trre i ˜ φ 2

2= 1

2 A[1+ cos(Δφ)]

€

IH = trte i ˜ φ 12

+ rrre i ˜ φ 22

= B

/2

Polarizer

Analyzer

+ = not

Spin based phase gratingSpin based phase grating

Coherence Measurements

Fussed Silica Wedgesused to move vertically one beam with respect to another Phase Flag

Neutron beam

To the detectors

Contrast measurements directly yields the coherence function

A neutron interferometer is a macroscopicA neutron interferometer is a macroscopic

quantum coherence device, we will measure quantum coherence device, we will measure

the coherence length of the neutrons wave-function.the coherence length of the neutrons wave-function.

€

η=1− λ2 Nbc

2π

€

coherence function

Γ Δ( ) = ψ 0( ) ψ Δ( )

Radius of neutron = 0.7 fmRadius of neutron = 0.7 fm

€

Δc =1

2δk≡ coherence length

δk ≡ spread in momentum

Coherent neutron scatteringCoherent neutron scattering

3-blade interferometer with 3-blade interferometer with

prisms to vertically shift the beam.prisms to vertically shift the beam.

€

ψout =12

ψ0 (z) + ψ0(z + Δ)( )

Adjust phase for only O-beam.Adjust phase for only O-beam.Add second interferometer.Add second interferometer.

€

IO Δ( )∝ S z( )∫ S z + Δ( )dz

S z( ) = N z( )bc z( )

First example of coherent neutron wave-funtion First example of coherent neutron wave-funtion over two interferometersover two interferometers

Interferometer

Neutron

Beam

Sample

Phase Shifter

Detectors

H-beam

O-beam

When will we have a neutron Interferometer at MIT?

Sample

Top View

Neutron wave functioncoherently split byBragg diffraction.

3Hedetectors

Phase Shifter

Δ

H-beam

O-beampath I

path II

10 cm

Each crystal blade acts as a beam splitter.


with vibrationswith vibrations

Vibrations change theVibrations change the

momentum of the n andmomentum of the n and

thus the Bragg angle.thus the Bragg angle.

Note, the twoNote, the two

paths changepaths change

in opposite in opposite

directions.directions.

€

IH ∝ 1− cos φ( )[ ]

€

IO ∝ 1+ cos φ( )[ ]

Even low frequency vibrations are deadly.Even low frequency vibrations are deadly.


with vibrationswith vibrations

€

IH ∝ 1− cos φ( )[ ]

€

IO ∝ 1+ cos φ( )[ ]

Low frequency vibrations are OK.Low frequency vibrations are OK.

No No interferenceinterference

€

τc = 50μs

υ c = 20kHz

Interferometer

Neutron

Beam

Sample

Phase Shifter

Detectors

H-beam

O-beam

When will we have a neutron Interferometer at MIT?

• • Multiple interferometers for controlling neutron information.Multiple interferometers for controlling neutron information.

• • Multiple paths to code for errors.Multiple paths to code for errors.

• • Spin dependent measurements to correct for momentum spread.Spin dependent measurements to correct for momentum spread.

Stern-Gerlach (details)

π/2 π/2π

Gradient magnets

AnalyzerPolarizer

Sample

Detector

II

III IV

V VI

x↑

)( xx2

1↓+↑

( ) ( ) )( xxexe2

1 xxixi ΔτΔστσ +↓+↑ +

( ) ( ) )( xxexe2

1 xxixi ΔτΔστσ +↑+↓ +

( ) ( ) )( xexe2

1 xxixi ↑+↓ + τΔστσ

( )[ ( ) ] xe xxxi ↑+− τΔστσ

( ) ( ) ( )[ ( ) ]∫ +−= Ωρ τΔστσ dexqS xxxi

where 2

m

vL

dxdB

x ⎟⎠⎞

⎜⎝⎛=γΔ

I

I

II

III

IV

V

VI

1998 1999 2000 2001 2002

J. C. Gore C. BreenS. Kumaresan

N. Seiberlich J. S. Hodges K. EdmondsJ. Yang

30 60 900.4

0.6

0.8

1

Noise Strength

Ent

angl

emen

t Fid

elit

y

Decoherence Free Subspace

22

12

211121 |2

|22

1|

2|

2|

2|

2 xyyxyx JNOTC −−−− −−−−−−=

Construction and Implementation of Logic Gates on two Spins

0

0.5

1

Quantum and Classical Channel

2003

A. GorshkovM. Henry

0

0

0 H

H( )n

H

Journal of Magnetic Resonance

Concepts in Magnetic Resonance

New Journal of Physics

Physical Reviews A

Center for Materials Science and Engineering Summer Students (NSF)

Physical Reviews A

2004

D. Khanal

EIT

Dr. Timothy Havel


Dr. Sekhar Ramanathan Dr. Sekhar Ramanathan Dr. Joseph EmersonDr. Joseph EmersonDr. Grum TeklemariamDr. Greg BoutisNicolas BoulantPaola Cappellaro Zhiying (Debra) ChenHyung Joon ChoDaniel Greenbaum Michael Henry Jonathan HodgesSuddhasattwa Sinha Jamie Yang

quantum information processing as told by: david g. cory department of nuclear science &...

Documents