Quantum information with cold atoms

Quantum information with cold atoms

Zheng-Wei Zhou( 周正威）

Key Lab of Quantum Information , CAS, USTC

October, 2009 KITPC

• Backgrounds on Quantum Computation(QC)• Quantum Computation(QC) and Quantum

Simulation(QS) with Cold atoms Standard model for QC

One-Way QC

QS for highly-correlated many body models

• Quantum Communication• Summary and Outlook

Outline

Backgrounds on Quantum Computation(QC)

Father of QC （ 1981 － 1985 ）

Elementary Gates for QC （ 1995 ）

A. Barenco (Oxford), C. H. Bennett (IBM), R. Cleve (Calgary), D. P. DiVincenzo (IBM), N. Margolus (MIT), P. Shor (AT&T), T. Sleator (NYU), J. Smolin (UCLA), H. Weinfurter (Innsbruck)

R. Feynman D. Deutsch

C. H. Bennett

Quantum Algorithms

1994

1997

Some Methods to Overcome Decoherence

（ 1 ） Quantum Error Correcting Codes（ Shor ， Steane ， Calderbank ， Laflamme ， Preskill ， etc. ）（ 1995 － 2000 ）

（ 2 ） Decoherence-Free Subspaces（ Duan, Guo, Zanardi, Whaley ， Bacon, Lidar, etc. ）（ 1997 － 2000 ）

（ 3 ） Dynamical Decoupling method（ Lolyd ， Viola ， Duan ， Guo, Zanardi ， etc. ） （ 1998 － 1999 ）

Standard Model for QC

Beyond Standard model (I)

• Topological Quantum Computing

A. Kitaev (1997)

Beyond Standard model (II)

• One Way Quantum Computing

R. Raussendorf H. Briegel (2000)

Beyond Standard model (III)

• Adiabatic Quantum Computation

Dorit Aharonov et. al (2004)

J. Goldstone et. al (2000)

E

t

......

Adiabatic QCStandard QC

P. Zoller

D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (1998)

Intermediate targets of QC——Simulating highly-correlated many body systems

D. Jaksch

Quantum Computer

Standard QC

model

Quantum Simulation

Adiabatic

QC

Beyond Classical Computer

Topological

QC

Deco

heren

ce, Scalab

ility, En

ergy g

ap,

etc

Once Fault-Tolerant QC can be realized…

Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms

Standard model for QC

One-Way QC

QS for highly-correlated many body models

Standard Model for QC

1. Register of 2-level systems (qubits)

The physical origin of the confinement of cold atoms with laser light is the dipole force:

Olaf Mandel, et al., Phys. Rev. Lett. 91, 010407 (2003)

2. Initialization of the qubit register

However, nonideal conditions will always result in defects in that phase (i.e., missing atoms and overloaded sites). How to suppress these defects in the lattice?

A possible approach is: the coherent filtering scheme.

P. Rabl, et al., Phys. Rev. Lett. 91,110403, (2003)

3 、 4. Tools for manipulation: 1- and 2-qubit gates and readout 1-qubit

1: Whether global operations are enough to implement universal quantum computation?

2: How to addressing single qubit in this system?

As far as ultracold atoms trapped in an optical lattice is concerned, global operations on atoms are available. However, addressing individual atom becomes very difficult. So, to implement universal quantum computation, we should answer the following questions:

OR

(S. Lloyd, Science 261, 1569 (1993); S. C. Benjamin, PRA 61, 020301R, 2000, PRL 88, 017904, 2002)

Some proposals for QC via global operations

Cellular-automata Machine

QC via translation-invariant operations

R. Raussendorf, Phys. Rev. A 72, 052301 (2005). K. G. H. Vollbrecht et al., Phys. Rev. A 73, 012324 (2006). G. Ivanyos, et al., Phys. Rev. A 72, 022339 (2005).Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).

In the above proposals, only translationally invariant global operations are required!

Redundant qubits (space and time overhead)

Initialization

Physical implementation

Shortcomings:

Bose Hubbard model

Ising Model

Type I

Type II

PRL 91,090402 (2003)

PRL 81, 3108 (1998); 90, 100401(2003); 91,090402 (2003)

Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).

(Effective periodic magnetic field induced by left and right circularly polarized light)

1D

2D

Addressing single qubit

Two-qubit operation

Z. W. Zhou, et al., Phys. Rev. A 74, 052334 (2006).

(Phys. Rev. A 70, 012306 (2004); Phys. Rev. Lett. 93, 220502 (2004))

Some proposals for QC via addressing single atom

Marked Qubit as Data-bus

Phys. Rev. A 70, 012306 (2004)

single-qubit rotation via multiqubit addressing

J. Joo, et al., PHYSICAL REVIEW A 74, 042344 (2006)

single-qubit rotation via Position-dependent hyperfine splittings

C. Zhang, et al., PHYSICAL REVIEW A 74, 042316 (2006)

the progress of experiments

Imaging of single atoms in an optical lattice

Nelson, K. D., Li, X. & Weiss, D. S. Nature Phys. 3, 556–560 (2007).

effective magnetic field results from the atom‘s vector light shift ：

Novel quantum gates via exchange interactions

Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in anoptical lattice. Nature 448, 452–456 (2007).

Science 319, 295–299 (2008).

Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008).

5. Long decoherence times

How many gate operations could be carried out within a fixed decoherence time?

“ For the atoms of ultracold gases in optical lattices, Feshbach resonances can be used to increase the collisional interactions and thereby speed up gate operations. However, the ‘unitarity limit’ in scattering theory does not allow the collisional interaction energy to be increased beyond the on-site vibrational oscillation frequency, so the lower timescale for a gate operation is typically a few tens of microseconds.”

“ Much larger interaction energies, and hence faster gate times, could be achieved by using the electric dipole–dipole interactions between polar molecules, for example, or Rydberg atoms; in the latter case, gate times well below the microsecond range are possible.”

I. Bloch, NATURE|Vol 453|19 June 2008|doi:10.1038.

Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms

Standard model for QC

One-Way QC

QS for highly-correlated many body models

R. Raussendorf H. Briegel

R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188, (2001)

Graph states

Graph States

Stabilizer code

For Example:1 32

1 2X Z

1 2 3Z X Z

2 3X Z

( 000 001 010 011 100 101 110 111 )L

Given a graph , the corresponding graph state is

Given a graph , the corresponding graph state is

A Controlled Phase Gate

D. Jaksch, et. al., Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett. 82, 1975 (1999).

Nature 425, 937 (2003)

Nature 425, 937 (2003)

New Journal of Physics 10 (2008) 023005

New Journal of Physics 10 (2008) 023005

Preparation of decoherence-free cluster states with optical superlattices

)2(cos)(cos)(

)2(cos)(cos)(

)()(

22

21

22

21

kyVkyVxV

kxVkxVxV

yVxVV

yyy

xxx

yx

Liang Jiang, et. Al., Phys. Rev. A 79, 022309 (2009)

Logical qubit in decoherence-free subspace

1,2 3,4

2,3 4,1

H

V

S S

S S

,

1

2i j i j i jS

0

2 11

23

V

V H

Here,

Logical qubit:

Implementing a C-Phase Gate

Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms

Standard model for QC

One-Way QC

QS for highly-correlated many body models

Cold Atoms Trapped in Optical Lattices to Simulate condensed matter physics

D. Jaksch, C. Bruder, C.W. Gardiner, J.I. Cirac and P. Zoller (1998)

Advantages as one of promising candidates of quantum simulations

Neutral atoms couple only weakly to the environment, allowing long storage and coherence times.

So far, cold atoms trapped in optical lattices is the only system in which a large number of particles can be initialized simultaneously.

Highly controllabilityControl of interaction strength with magnetic field (Feshbach Resonance)Various geometry of optical latticesControllable tunneling ratesBosons, Fermions, or mixture

Bose-Hubbard Model

Effective highly-correlated many body models

Two-component Bose-Hubbard Model

Feshbach resonance -- magnitudeOptical lattice -- diversity Experiments: Ketterle, Esslinger etc.

• Weakly interacting fermions in an optical lattice

-- single-band Hubbard model (Hofstetter et al, PRL 2003)

i

iiiijji

iweak aaaauaatH ,

• Strongly (resonantly) interacting fermions in optical lattice

-- Boson-fermion Hubbard model ??

i

iiii

iionweakstrong bbaabgHH

Stoof, Holland, Zhou, etc., 2005 Inadequate!

Fermions in an Optical Lattice

• Multi-band populations (T.-L. Ho, cond-mat/0507253; 0507255, PRL 2006)

i

iiii

iionweakstrong bbaabgHH

Why is it inadequate?

~bgon Eg

Band gapOn-site coupling rate

tgoff • Off-site collision couplings (L.-M. Duan, PRL 95, 243202,2005)

Off-site coupling rate

Tunneling rate

Off-site coupling

toffg

ir

pqriiqippqr aabg

;Different bands

Strong interaction effects

• Starting point: the field Hamiltonian

•Keep all the bands

•Keep the off-site couplings

L.-M. Duan, PRL 95, 243202,2005

• Limiting case2: molecule limit

• Limiting case 1: atom limit

Quantum simulation with polar molecules

A. Micheli, G. K. Brennen and P. Zoller, A toolbox for lattice-spinmodels with polar molecules, Nature Physics, 2, 341 (2006)

• Time-of-flight imaging

expansion

tt rr density

mktrrt /0

condensate

Diagonal correlation in momentum space

kk

Detection of ultracold atoms

One can also utilize density-density correlations in the image of an expanding gas cloud to probe complex many-body states.

Nature Physics, 4, 50 (2008)

Nature Physics, 4, 50 (2008)

Quantum Simulation

Quantum Computer

Limits from classical world

Starting point

Quantum Communication Why long-distance quantum communication is so difficult?

Transmission loss/fidelity of entanglement—decreasing exponentially with the length of the connecting channel

Solution: Quantum repeater combining entanglement swapping and purification [H. Briegel et al., Phys. Rev. Lett. 81, 5932 (1998)]

Atomic-ensemble-based quantum memory is used to transfer the photonic states to the excitation in atomic internal states so that it can be stored, and after the storage of a programmable time, it should be possible to read out the excitation to photons without change of its quantum state.

M.D. Lukin et al., Phys. Rev. Lett. 84, 4232 (2000); M. Fleischhauer and M.D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).

Atomic-ensemble-based quantum memory

Physical implementation of Quantum Repeater:

A Scheme based on atomic ensembles, the DLCZ scheme

[L.-M. Duan et al., Nature 414, 413 (2001)]

The phase stability problem in the DLCZ scheme

In the DLCZ protocol, two entangled pairs are generated in parallel. The relative phase between the two entangled states has to be stabilized during the entanglement generation process.

As entanglement generation process is probabilistic. The experiment has to be repeated many times to ensure that there is a click at the detectors. The two phases achieved at different runs of the experiments are usually different due to the path length fluctuations in this time interval.

A robust, fault-tolerant quantum repeater

•a) Local preparation of entanglement (at adjacent nodes) by a linear-optical polarization entangler and then entanglement swapping

•(b) Entanglement connection

•(c) Linear-optical entanglement purificationB. Zhao, Z.-B.Chen. et al., Phys. Rev. Lett, 98, 240502 (2007); Z.-B.Chen. et al., Phys. Rev. A 76, 022329 (2007).

Summary and Outlook

Quantum Computation(QC) and Quantum Simulation(QS) with Cold atoms

Standard model for QC

One-Way QC

QS for highly-correlated many body models

Quantum Communication

Lowering the temperatureAchieving single-site addressing