Wave Physics PHYS 2023 Tim Freegarde. 2 2 Beating TWO DIFFERENT FREQUENCIES.
Coherent cooling: a momentum state quantum computer Tim Freegarde Dipartimento di Fisica,...
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Tim Freegarde Dipartimento di Fisica, Università di Trento, 38050 Povo, Italy Quantum Optics & Laser Science, Imperial College, London SW7 2BZ, UK Danny Segal • • • • • • • • • • • • Matrices • Non-zero elements cluster around leading diagonal • m i,j and m i+2n,j+2n differ only through momentum dependence • Matrices therefore summarized as 4x4 elements: G(t) leve l name description sequence basi c G(t/) W - (,0) . FG(t/4) . W - (,0) . FG(t/4) . W + (,0) . FG(t/4) . W + (,0) . FG(t/4) 1 qubi t NOT(0) invert lsb F(/2) . W + (/2,0) . F(/2) CP1(0) if state=0, invert phase F() . W + (,0) HAD(0) Hadamard on Q 0 W + (/4, /4) . F() W + (,0) 2 qubi t EX(1,0) exchange Q 1 , Q 0 F(/2) . W - (/4, ) . G(/4) . W - (/4, /4) . F(5/4) XOR(1,0 ) CNOT Q 1 , Q 0 F(/2) . W + (/4, ) . G(/4) . W + (/4, /4) . F(5/4) CP2(0) if state=0, invert phase F(3/4) . G(/4) . W + (, ) • Laser cooling may be achieved through the coherent manipulation of two-level atoms between discrete one- dimensional momentum states • This is formally equivalent to a 'momentum state quantum computer‘ • Qubits form the binary representation of the momentum state • Operations are combinations of laser pulses with kinetic energy dependent free phase evolution • The logical invert, exchange, XOR and Walsh-Hadamard operations can be performed on any qubits, as well as conditional phase inversion • These allow a binary right-rotation, which halves the width of the ground state momentum distribution in a single coherent process • The problem of field design for the coherent control of atomic momenta may thus be tackled using techniques from quantum information processing Bloch vectors g e mixture pure stat e pure stat e radiative interaction free evolution • • • • • • • • • • • • Candidate ‘toy’ system • Size scales with number of states, so number of qubits limited • Practical implementation using stimulated Raman transitions between hyperfine levels • Extension to 2-D for parallel computing QUANTUM COMPUTING COHERENT COOLING • Offers maximum narrowing of momentum distribution within coherent process • Imperfect application nonetheless cools non-integer momenta • Complex optical pulse sequences related to ‘coherent control’ fields FUTURE ALGORITHMS • Grover-type search for cold states • More complex entanglement (>2 states) cos i e - i sin 0 0 0 0 0 0 i e i sin cos 0 0 0 0 0 0 0 0 cos i e - i sin 0 0 0 0 0 0 i e i sin cos 0 0 0 0 0 0 0 0 cos i e - i sin 0 0 0 0 0 0 i e i sin cos 0 0 0 0 0 0 0 0 cos i e - i sin 0 0 0 0 0 0 i e i sin cos p 0 + 4k p 0 + 3k p 0 + 2k p 0 + k p 0 p 0 - k p 0 - 2k p 0 - 3k
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Transcript of Coherent cooling: a momentum state quantum computer Tim Freegarde Dipartimento di Fisica,...
Tim Freegarde
Dipartimento di Fisica, Università di Trento, 38050 Povo, Italy
Quantum Optics & Laser Science, Imperial College, London SW7 2BZ, UK
Danny Segal
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Matrices
• Non-zero elements cluster around leading diagonal
• mi,j and mi+2n,j+2n differ only through momentum dependence
• Matrices therefore summarized as 4x4 elements:
G(t)
level name description sequence
basic G(t/) W-(,0) . FG(t/4) . W-(,0) . FG(t/4) . W+(,0) . FG(t/4) . W+(,0) . FG(t/4)
1 qubit NOT(0) invert lsb F(/2) . W+(/2,0) . F(/2)
CP1(0) if state=0, invert phase F() . W+(,0)
HAD(0) Hadamard on Q0 W+(/4, /4) . F() W+(,0)
2 qubit EX(1,0) exchange Q1, Q0 F(/2) . W-(/4, ) . G(/4) . W-(/4, /4) . F(5/4)
XOR(1,0)
CNOT Q1, Q0 F(/2) . W+(/4, ) . G(/4) . W+(/4, /4) . F(5/4)
CP2(0) if state=0, invert phase F(3/4) . G(/4) . W+(, )
HAD(1,0)
Hadamard on Q1, Q0 EX(1,0) . HAD(0) . EX(1,0) . HAD(0)
• Laser cooling may be achieved through the coherent manipulation of two-level atoms between discrete one-dimensional momentum states
• This is formally equivalent to a 'momentum state quantum computer‘
• Qubits form the binary representation of the momentum state
• Operations are combinations of laser pulses with kinetic energy dependent free phase evolution
• The logical invert, exchange, XOR and Walsh-Hadamard operations can be performed on any qubits, as well as conditional phase inversion
• These allow a binary right-rotation, which halves the width of the ground state momentum distribution in a single coherent process
• The problem of field design for the coherent control of atomic momenta may thus be tackled using techniques from quantum information processing
Bloch vectorsg
e
mixture
pure state
pure state
radiative interaction
free evolution
•
•
• •
•
•
•
•
•
•
•
• Candidate ‘toy’ system• Size scales with number of states, so number
of qubits limited• Practical implementation using stimulated
Raman transitions between hyperfine levels• Extension to 2-D for parallel computing
QUANTUM COMPUTING
COHERENT COOLING
• Offers maximum narrowing of momentum distribution within coherent process
• Imperfect application nonetheless cools non-integer momenta
• Complex optical pulse sequences related to ‘coherent control’ fields
FUTURE ALGORITHMS
• Grover-type search for cold states• More complex entanglement (>2 states)
cos i e-isin 0 0 0 0 0 0
i eisin cos 0 0 0 0 0 0
0 0 cos i e-isin 0 0 0 0
0 0 i eisin cos 0 0 0 0
0 0 0 0 cos i e-isin 0 0
0 0 0 0 i eisin cos 0 0
0 0 0 0 0 0 cos i e-isin0 0 0 0 0 0 i eisin cos
p0 + 4k
p0 + 3k
p0 + 2k
p0 + k
p0
p0 - k
p0 - 2k
p0 - 3k
