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One-way quantum computation with ultra-narrow optical transition of                                                                                                                                                                                                    171
                                                                                                                                                                                                                                                                             Yb atoms                                                       (Mo-105)
Akimasa Nakamoto1,*, Martin Miranda1, Yuki Okuyama1, Atsushi Noguchi1,†, Masahito Ueda2, and Mikio Kozuma1
1. Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo, Japan
2. University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan
*nakamoto.a.aa@m.titech.ac.jp, †Present Affiliation: Osaka University

    1. Our plan                                                                                                                                                                                     2. Review:
                                                                                                                                                                                                                 Conventional technique for making a cluster state for electron spins
        We are planning to implement a quantum computer with 171Yb atoms which have nuclear spin of                                                                                                 A cluster state has been successfully created for Rubidium atoms through controlled collisions
        1/2 in the ground state. Magnetic moment of the nuclear spin is 2000 times smaller than that of                                                                                             which was implemented by using electronic spin dependent optical potential[2].
        the electronic spin. This fact leads to a merit of long coherence time, but also makes it diffcult to
        realize two qubits gate operation using dipole-dipole interaction.
                                                                                                                                                                                           e-
                                                                                                                                                                                                                                                                                                                                        
                                                                                                                                                     e-
                                                                                                                                                                    171
                                                                                                                                                                          Yb
        Our strategy: Cluster computation
                                                                                                                                                                                                                                                                                                                                        
        Why: Only one time qubits interaction is required.                                                                                                             [Xe]4f 6s      14        2



         To implement a one-way quantum computation
                                                                                                                                                                                                                                                                                                                                        
                                         Operation 1.
                                         Produce highly entangled multi-particle states (Cluster states)
                                                                                                                                                                                                                                                           Fine   Detuning   Hyperfine  
                                                         C
                                                                       2 
                                                                                            3 
                                                                0 1 z  1 1 0 2  z  1 2  0               n 1
                                                                                                                        z  1 n 1  0 n  1 n 
                                                                                                                           n 


                                                                                                                                                                                                                   Hyperfine                                                                                   2
                                                                                                                                                                                                                                                                                                                   P3/2
                                         Operation 2.                                                                                                                                               Fine           500 MHz
                                                                                                                                                                                                    300 GHz                                                                    Detuning   Hyperfine
                                         Apply unitary transformation and observe each qubit in sequence.                                                                                                                                                                                                      2
                                                                                                                                                                                                                                                                                                                   P1/2
                                                                                                                                                                                                                    800 MHz
                                                                                                                                                                                                                                                                              Hyperfine                                                               

                                                                                                                                                                                                                                                                              dependency is lost
          [1]Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188-5191 (2001).                                                                                                                      J I
                                                                                                                                                                                                                                      1 3
                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                   S1/2
                                                                                                                                                                                                                                                                                                                   2
                                                                                                                                                                                                                                      2 2                                                                                                            1              1
                                                                                                                                                                                                                                                    J I                                                                                     mj          mj  
                                                                                                                                                                                                                                                
                                                                                                                                                                                                                                                    1 3
                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                                                     2              2

                                  How to realize qubits interaction?
                                                                                                                                                                                                                                                    2 2

                                                                                                                                                                                                     [2] Olf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Haensch & Immanuel Bloch, Controlled collisions for multi-particle
                                                                                                                                                                                                     entanglement of optically trapped atoms, Nature 425, 937-940 (2003)



   3. How to make nuclear spin dependent potential?                                                                                                                                                 4. How to realize qubits interaction?
    Comparison of two approaches to make an optical lattice (Potential depth 10μK, Life time 1 sec).                                                                                                                                                                                                                         μm=2.7μB
                                                                                                                                                                                                    In the nuclear spin dependent potential,
                                                                       Hyperfine                                   3                  1              1             3                                                                                                                                                   3                                            3
                                                                                                                                                                                                                                                                                                          mF '                                         mF '  
                       Γ/ 2π = 29 MHz                                  350 MHz                            mF '           mF '         mF '          mF '                                    superposition between S0 and a small
                                                                                                                                                                                                                                      1

              P1
              1                                                        F’ = 1/2
                                                                                         3
                                                                                             P2                    2                  2              2             2
                                                                                                                                                                                 F’ = 3/2                                                                                           3
                                                                                                                                                                                                                                                                                     P2(F’ = 3/2)
                                                                                                                                                                                                                                                                                                                       2                                            2


          399 nm
                                                                       F’ = 3/2          507 nm                                                                                                     amount of P2 is generated.
                                                                                                                                                                                                                   3
                                                   Detuning                                                                                                               Hyperfine
                                                   -75 THz
          443 nm

                                                                                                                                                                                F’ = 5/2
                                                                                                                                                                                                     0  mF 1/ 2  1 / 2   mF '3 / 2  3 / 2                                                                                                     
          Power 1W                                                                       Power 400mW                                                                                                 1  mF 1/ 2  1 / 2   mF '3 / 2  3 / 2                                                  S0(F = 1/2)
                                                                                                                                                                                                                                                                                                    1

          Waist 60μm                                                                     Waist 30μm                                                                                                                                                                                                                                 1                1
                                                                                                                                                                                                                                                                                                                           mF             mF  
                                                                                                                                                                                                                                                                                                                                    2                2

                                                        
                                                                                                                                                       
              S0
              1
                                mF  
                                         1
                                         2
                                             mF  
                                                      1
                                                      2
                                                                                         S0
                                                                                         1
                                                                                                                                      1              1
                                                                                                                           mF           mF  
                       Hyperfine dependency is lost                                                                                   2              2
                                                                                                                                                                                                                                 r
              P1
              1                                                                                           Hyperfine   Detuning                                                                                   1                        0                                               To achieve a π phase shift:
              399 nm
                                                                                                         6.6 GHz                  -1 MHz                      25 mHz                                                           0  m       4
                                                                                                                                                                                                                                                               2                                r = 30 nm,
              443 nm
                                                                                                                                                                                                             Enegy Shift ~  
                                                                                                                                                                                                                               4 r 3                                                           Power = 400 mW, Waist = 30μm,
                                                                                              Ultra-narrow optical transition is very useful                                                                                                                                                    Detuning = 2π × 1 MHz,
                                                                                              for preparing a nuclear spin dependent                                                                                                                                                            Potential = 4 μK (17Er),
                                                                                              potential!                                                                                                                                                                                        ρee = |ε|2 = 0.07,
              S0
              1
                                                                                                                                                                                                                                                                                                Interaction Time = 5 ms.
                                         J=0


    5. Coherence time vs interaction time                                                                                                                                                            6. Single site access
    When we create a cluster state, mixing between the 1S0 and 3P2 states is required. However,                                                                                                      By focusing a far detuned laser light into a specific site, a light shift can be
    such a mixing leads to decoherence of the qubit, since the 3P2 state has a large magnetic                                                                                                        induced. The pumping light, with its wavelength of 507nm, excites the single
    moment. By changing the detuning of the lattice beam by factor of ∼ 8 MHz, we can                                                                                                                atom in that specific site to the 3P2 metastable state in a spin dependent manner.
    switch off such mixing, while                                                                                                                                                                    Using the cyclic transition
                                                                               (sec)
    maintaining the lattice potential,                                                         Cluster interaction time                                                                              between 3P2 and 3D3 states
                                                                                    10                                                                                                                                                                                                  D3
                                                                                                                                                                                                                                                                                        3
                                                                                                                                                                                                                                                                                                            5 MHz
    since the potential is induced by S0                         1
                                                                                                                                                                                                     (494nm), we can collect
                                                                                     1                                                                                                                                                                                              494 nm
    to P1 transition.
          1
                                                                                                                                                                                                     fluorescence from the atom and
                                                                                                                        Decoherence time
                                                                                   0.1                                                                                                               perform the projective                                        P2
                                                                                                                                                                                                                                                                   3                                                                                          25 mHz

    P1
    1                                                                             0.01                                                                                                               measurement.
                        28 MHz
                                                                               0.001                                                                                                                                                                                                                                                                       x
                                                                                                                                                                       (MHz)
                                                                                                     2                 4                    6                   8         10
                                                                                    0
                                                               5 MHz
        399 nm                                 D3
                                               3
                                                                                    -2                        Potential due to 1S0 -> 3P2

                                                      3
                                                          494 nm
                                                          P2     25 mHz
                                                                                    -4
                                                                                    -6
                                                                                                                                                                                                     Related presentation
                                                      3
                                                          P1     181 kHz            -8                                                                                                                                                              Tu-107 “Resolution assessment of a fluorescence microscope for observing
                             507 nm                                                -10                                                                                                                                                              single ytterbium atoms trapped in two-dimensional optical lattice”
                              556 nm
                                                      3
                                                          P0
                                                                                   -12
                                 578 nm
                                                                                   -14                       Potential due to 1S0 -> 1P1                                                                                                            Th-105 “All optical formation of Ytterbium two-dimensional
              1
                  S0
                                                                               (μK)                                                                                                                                                                 quasi-condenstate near surface of solid immersion lens”
                                                                                         Interaction ON                                                   Interaction OFF

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One-way quantum computation with ultra-narrow optical transition of 171Yb atoms

  • 1. One-way quantum computation with ultra-narrow optical transition of 171 Yb atoms (Mo-105) Akimasa Nakamoto1,*, Martin Miranda1, Yuki Okuyama1, Atsushi Noguchi1,†, Masahito Ueda2, and Mikio Kozuma1 1. Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo, Japan 2. University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan *nakamoto.a.aa@m.titech.ac.jp, †Present Affiliation: Osaka University 1. Our plan 2. Review: Conventional technique for making a cluster state for electron spins We are planning to implement a quantum computer with 171Yb atoms which have nuclear spin of A cluster state has been successfully created for Rubidium atoms through controlled collisions 1/2 in the ground state. Magnetic moment of the nuclear spin is 2000 times smaller than that of which was implemented by using electronic spin dependent optical potential[2]. the electronic spin. This fact leads to a merit of long coherence time, but also makes it diffcult to realize two qubits gate operation using dipole-dipole interaction. e-  e- 171 Yb Our strategy: Cluster computation  Why: Only one time qubits interaction is required. [Xe]4f 6s 14 2 To implement a one-way quantum computation  Operation 1. Produce highly entangled multi-particle states (Cluster states)  Fine   Detuning   Hyperfine    C  2   3   0 1 z  1 1 0 2  z  1 2  0   n 1  z  1 n 1  0 n  1 n  n  Hyperfine 2 P3/2 Operation 2. Fine 500 MHz 300 GHz  Detuning   Hyperfine Apply unitary transformation and observe each qubit in sequence. 2 P1/2 800 MHz Hyperfine    dependency is lost [1]Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188-5191 (2001). J I 1 3   S1/2 2 2 2 1 1 J I mj   mj    1 3  2 2 How to realize qubits interaction? 2 2 [2] Olf Mandel, Markus Greiner, Artur Widera, Tim Rom, Theodor W. Haensch & Immanuel Bloch, Controlled collisions for multi-particle entanglement of optically trapped atoms, Nature 425, 937-940 (2003) 3. How to make nuclear spin dependent potential? 4. How to realize qubits interaction? Comparison of two approaches to make an optical lattice (Potential depth 10μK, Life time 1 sec). μm=2.7μB In the nuclear spin dependent potential, Hyperfine 3 1 1 3 3 3 mF '   mF '   Γ/ 2π = 29 MHz 350 MHz mF '   mF '   mF '   mF '   superposition between S0 and a small 1 P1 1 F’ = 1/2 3 P2 2 2 2 2 F’ = 3/2 3 P2(F’ = 3/2) 2 2 399 nm F’ = 3/2 507 nm amount of P2 is generated. 3 Detuning Hyperfine -75 THz 443 nm F’ = 5/2 0  mF 1/ 2  1 / 2   mF '3 / 2  3 / 2   Power 1W Power 400mW 1  mF 1/ 2  1 / 2   mF '3 / 2  3 / 2 S0(F = 1/2) 1 Waist 60μm Waist 30μm 1 1 mF   mF   2 2     S0 1 mF   1 2 mF   1 2 S0 1 1 1 mF   mF   Hyperfine dependency is lost 2 2 r P1 1  Hyperfine   Detuning   1 0 To achieve a π phase shift: 399 nm 6.6 GHz -1 MHz 25 mHz 0  m 4 2 r = 30 nm, 443 nm Enegy Shift ~   4 r 3 Power = 400 mW, Waist = 30μm, Ultra-narrow optical transition is very useful Detuning = 2π × 1 MHz, for preparing a nuclear spin dependent Potential = 4 μK (17Er), potential! ρee = |ε|2 = 0.07, S0 1 Interaction Time = 5 ms. J=0 5. Coherence time vs interaction time 6. Single site access When we create a cluster state, mixing between the 1S0 and 3P2 states is required. However, By focusing a far detuned laser light into a specific site, a light shift can be such a mixing leads to decoherence of the qubit, since the 3P2 state has a large magnetic induced. The pumping light, with its wavelength of 507nm, excites the single moment. By changing the detuning of the lattice beam by factor of ∼ 8 MHz, we can atom in that specific site to the 3P2 metastable state in a spin dependent manner. switch off such mixing, while Using the cyclic transition (sec) maintaining the lattice potential, Cluster interaction time between 3P2 and 3D3 states 10 D3 3 5 MHz since the potential is induced by S0 1 (494nm), we can collect 1 494 nm to P1 transition. 1 fluorescence from the atom and Decoherence time 0.1 perform the projective P2 3 25 mHz P1 1 0.01 measurement. 28 MHz 0.001 x (MHz) 2 4 6 8 10 0 5 MHz 399 nm D3 3 -2 Potential due to 1S0 -> 3P2 3 494 nm P2 25 mHz -4 -6 Related presentation 3 P1 181 kHz -8 Tu-107 “Resolution assessment of a fluorescence microscope for observing 507 nm -10 single ytterbium atoms trapped in two-dimensional optical lattice” 556 nm 3 P0 -12 578 nm -14 Potential due to 1S0 -> 1P1 Th-105 “All optical formation of Ytterbium two-dimensional 1 S0 (μK) quasi-condenstate near surface of solid immersion lens” Interaction ON Interaction OFF