Quantum Computation with Cold Polar Molecules

1
Quantum Computation with Cold Polar Molecules
Ying-Cheng Chen Physics Astronomy, Rice
University
2
Outline

• Overview of laser cooling and trapping of atoms.
• Introduction of quantum computation.
• Quantum Computation with cold polar molecules.
• Generation of cold molecules.
• Additional research opportunities.
• Conclusions.

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Laser Cooling of Atoms

• Momentum is imparted to an atom when it scatters
  light from a laser.
• This can slow or stop atoms in a beam.
• With a proper setup (magneto-optical trap, MOT),
  atoms can be trapped and cooled to mK
  temperatures or less.

4
Chronological Landmarks of Cold Atom Study

• 1985 First demonstration of laser cooling of
  atoms
• 1987 Magneto-optical trap
• 1988 Sub-Doppler cooling, VSCPT cooling down to
  1 ?K
• 1989 Atomic fountain clock
• 1990 Raman cooling down to 1 nK
• 1993 Dark MOT increases the MOT density
• 1994 Evaporative cooling in a magnetic trap
• 1995 Bose Einstein condensation
• 1997 Atom laser, Matter wave interference (Nobel
  Prize issued for Laser cooling)
• 1998 Feshbach resonance in a BEC, Cold molecule
  formation in a MOT, Four-wave mixing in a BEC
• 1999 Degenerate Fermi gas, Ultracold neutral
  plasma
• 2000 Spontaneous evolution from Rydberg gases to
  ultracold plasmas
• 2001 Vortex in a BEC, BEC on an atom chip, Stop
  light in cold atom(Nobel Prize issued for BEC)
• 2002 Quantum phase transition, Molecular BEC,
  Bright soliton in BEC
• 2003 Demonstration of quantum entanglement by
  BEC in optical lattices...
• 2004 Superfluidity of an atomic Fermi gas.

The first decade development stage, the second
decade application stage !
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Many Beautiful Experiments with Cold Atoms
More than 130 atom cooling groups worldwide!
www.uibk.ac.at/c/c7/c704/ultracold/atomtraps.html
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Impact of Cold Atoms on Different Fields

• Atomic, molecular and optical (AMO) Physics
• Atom Optics
• Quantum Optics
• Metrology
• Traditional Atomic Physics
• Condensed-Matter Physics
• Plasma Physics
• Quantum Information Science
• Chemistry

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Goals for Different Stages

• Short-term (3 years)
• Development of molecules cooling and trapping
  technologies.
• Middle-term (410years)
• Studying condensed-matter physics with cold
  polar molecules in optical lattices.
• Developing different toolbox for different
  aspects of quantum computing.
• Long-term (gt10 years)
• Demonstration of quantum computation/informati
  on in Taiwan.

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Quantum Computation, Concepts
Input
Output
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Quantum Computation, Concepts (cont.)

• Qbits bits are coherent quantum states.
• e. g. two qbits
• Decoherence time how long will the coherent
  quantum state last?
• All quantum operations can be realized by (1995)
• one-bit gate (unitary operation)
• two-bit universal quantum gate (e.g. C-NOT).
• (Quantum entanglement)

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Quantum Computation, Concepts (cont.)

• Quantum parallelism Simultaneous processing of
  many possibilities, the reason why QC is faster
  than classical QC.
• Scalable QC system Easy to increase the number
  of quantum gates,
• but also need to address individual gate.

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Quantum Computation, Softwares

• Quantum algorithms
• Shor(1994) factorization of prime number
• Grover(1997) quantum database search
• Error-correction Fault-tolerant
  computation(1995)
• Protect quantum information against noise.
• Reliable quantum computation even with
  non-perfect quantum gates.

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Difficulties of Quantum Computation

• Requires two almost mutual-exclusive conditions.
• Experimental effort to gain strong, precise
  control over quantum systems that maintain their
  quantum nature.

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DeVincenzo Criteria (2001)
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Quantum Computation, Physical Realization
http//qist.lanl.gov the quantum computation
roadmap
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Neutral Atom QC Roadmap
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Quantum Computation with cold Polar Molecules in
an Optical Lattice
V (3kV)
E-field due to dipole of its neighbors
Optical lattice,1W 1064nm NdYAG laser Trap depth
100 ?K
-V
KCs polar molecule (104 total )
5 mm
PRL 88,067901,2002
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Other Proposals Utilizing Optical Lattices

• Laser induced electric dipole-dipole interaction.
• (Jessen et. al. PRL 82, 1060, 1999)
• Controlled collisions between atoms.
• (Zoller et. al .PRL 82, 1975, 1999. Nature
  425, 937, 2003)
• Electric dipole-dipole interaction of Rydberg
  atoms.
• (Jaksch et. al. PRL 85, 2208, 2000)
• Magnetic dipole-dipole interactions.
• (Derevianko et. al. quant-ph/0406117)

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Features of the Proposed Approach

• Long decoherence time 1 s or longer.
• Easy to scale up the number of quantum gates.
• Easy to address individual qubit due to
  introduced E-field gradient.
• Involved technologies are all achievable (but
  challenging).

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Controlled-NOT Gate
Energy
?-pulse at
E-field off
E-field on
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Estimation of Characteristic Values
Resonant frequency
3.5-6.0 GHz for Eext2-5 kV/cm
Resonant frequency difference per lattice site
250kHz
CNOT Gate time
For a microwave ? pulse, required field strength
10 mV/cm
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Production of Polar Molecules by Photoassociation

• 1998, molecules (Cs2) formation by
  photoassociation. T10?K.
• Polar molecules, KRb, RbCs have been produced by
  photoassociation.(PRL 92,153001,2004 and PRL
  92,133203,2004)
• Production rate 1.5?108
• s-1 rate for RbCs was obtained.
• Need some works to prepare population in the
  absolute vibrational ground state.

K 4SCs 6P1/2
895nm
K 4SCs 6S
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Stark Molecules Cooling

• Stark electric cooling (PRL 83, 1558, 1999)

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Buffer Gas Molecules Cooling

• Buffer gas cooling (Nature 395, 148, 1998)

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Molecule Trapping

• Trapping by magnetic dipole. (Nature 395, 148,
  1999)
• Trapping the low-field seeking molecules by
  electrostatic trap.(Nature 406, 491, 2000 and
  Nature 411, 174, 2001)
• Trapping both LFS and HFS molecules by AC
  electric trap. (PRL 92, 223001, 2004)
• Proposal of microwave trap. (physics/0407038)
• Evaporative cooling maybe necessary to produce
  cold enough temperature.

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Loading the Optical Lattice

• Trapping of Cs2 molecules in an optical dipole
  trap. (PRL, 81,5105,1998).
• Loading two-species BEC to an optical lattice,
  achieving a Mott-insulator
• phase with exactly one atom one species per
  site, photoassociating them to produce one polar
  molecule per site. (PRL 90,110401,2003).

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Superfluid-Mott Insulator Quantum Phase Transition
Coherent State
Increase the trap depth
Fock State
Nature, 415, 39, 2002
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State Preparation and Detection

• Preparation
• Initially, all qubits are in 0gt state. Use
  microwave transition to drive qubits to desired
  states.
• Detection
• State-selective, resonant multiphoton ionization
• RF ? pulse to transfer the population and
  perform the same measurement
• imaging detection of the resulting ions and
  electrons by ion optics and microchannel plate.
  (gt90 efficiency )

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Issues

• Non-nearest neighbor coupling can be eliminate
  by a refocusing procedure as in NMR QC.(PRA,
  61,042310,2000)
• How to entangle two non-nearest-neighbor qubits ?

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Issue of Nearest Neighbor Interaction Only
Quant-ph 0402196
Factorize an integer N (with binary length L),
requires 2L4 qubits, 8L4(first order) gates
arranged in a circuit of depth 32L3(first order).
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Future Possibilities

• More species of cold molecules can be loaded by
  electric slowing and trapping, in combination
  with evaporative cooling. (Middle-term)
• Macrofabricated electric trap. (Collaboration)
• Nondestructive detection by nearby
  single-electron transistors.(Collaboration)

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Additional Research Opportunities

• Condensed-matter physics
• BCS-like superfluid.(PRA 66,013606,2002),
  supersolid and checkerboard states (PRL 88,
  170406, 2002)
• Search for violations of fundamental symmetries,
  electron dipole moment (EDM) (J. Phys. B 28,1933,
  1995.)
• Ultracold molecular collision (Chem. Phys. Lett.
  341,652, 2001)
• Ultracold chemical reaction (J. Chem Phys.
  116,9222,2002)

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Budget Assessment

• Cold CsK MOT, 5 millions NTD
• (Lasers, vaccum, optics, electronics..)
• Stark molecules cooling development, 4 millions
  NTD
• (High voltage power supply, Cooling system.)
• Molecules trapping development, 4 millions
• (RF trapping Optical lattice)
• Quantum Control support, 3 millions

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Cooperation Opportunities

• Quantum control of chemical dynamics and
  reaction.
• Cold molecules collisions and reactions.
• Condensed matter physics with cold molecular
  gases in optical lattices.
• Theoretical atomic physics.

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Conclusions

• We have to start experimental study of quantum
  information science in Taiwan now!

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Some Words from Ketterle

• the major challenge for a young scientist is to
  make the right decision about which hill to climb

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Shors Algorithm

• To find factors of a composite number N that has
  two prime factors p, q.
• Step 1 Randomly choose an element A lt N
• Step 2 If dgcd(A,N) gt 1
• then d is a non-trivial factor of
  N
• Step 3 if d 1 extract the order/periodicity
  (r)
• such that ArN 1
• ? N divides Ar-1
• ? N divides (Ar/2-1) (Ar/21)
• Step 4 Find that factor using Euclids
  Algorithm
• d1gcd( Ar/2-1,N ) OR d2gcd(
  Ar/21,N )

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Factorize 15

• Z15 2,3,4,14 is the set of elements that can
  be tried.
• Step 1 Chose some A and find its order ( r )
  from the standard basis using A,A2,,AnN.
• Let A2 then,
• 215, 415, 815, 1615, 3215
• 2, 4, 8, 1, 2
• Order/period ( r ) 4.
• Step 2 Find Ar/2-1, Ar/21
• 24/2-1, 24/21 gt 3, 5 are possible factors.

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Factorize 35

• Let A2
• Step 1 235, 2235, 2335, ,21335
• Step 2 2,4,8,16,32,29,23,11,22,9,18,1,2
• Order ( r ) 12
• Step 3 212/2-1, 212/21 gt 63, 65
• Step 4 Find gcd(63,35) recursively using
  Euclids method.
• First divide smaller number into the larger
  number.
• 63/35 1(28/35) 35/28 1(7/28) 28/7
  4(0)
• gcd(63,35) 7 which is one of the factors of
  35.

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Shors Algorithm on a Quantum Computer

• Take two registers R1, R2 each of length
  q-qubits.
• Step 1 Initialize R1 into superposition of
  q-qubits. Then R1 contains all numbers
  a0,1,2,..2q-1
• Step 2 Choose a number A at random and compute
• Aa N for all a and place them in R2.
• Numbers in R2 will be periodic with order ( r
  ).
• Step 3 Perform Fourier-Transforms on R1 and
  measure the content. The content has a very high
  probability to be r.
• Step 4 Use Euclids algorithm to check the
  factors.