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Optical Resources for Quantum Information Processing

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					Optical Resources for Quantum
    Information Processing
            PGK
                          Outline
1. Sources
    •   Ultrabright entanglement source
    •   Hyper-entanglement
2. Storage
    •   “Long”-time
    •   Switchable
3. Detectors
    •   High-efficiency photon counters
    •   Upconversion


   Some photos courtesy of Google Image
   Search: “Quantum Products”
Spontaneous Parametric Downconversion
 Two qubits: Two-crystal Source


                                        V-polarized
                                         (from #2)


               #2




              Maximally-entangled state
Tune pump polarization:      Add decoherence to arms
 Nonmax. entangled states    (Partially) mixed states
Non-degenerate Polarization-entanglement
                       H-polarized
          #1 #2                             V-polarized
                       (from #1)
                                            (from #2)
 351nm
                                             737 nm



                                        670 nm
             1 (
         y =     H H + eij V V )
             2
 Re               Im                 F with HH+VV = 0.968

                                     Linear entropy = 0.027

                                     Tangle = 0.957
The problem…
                                 100
  Fidelity with Bell State (%)

                                 99
                                 98
                                 97
                                 96
                                 95
                                 94
                                 93
                                 92        Uncompensated
                                 91
                                           Compensated
                                 90
                                       2    4       6         8       10   12
                                                 Iris Diameter (mm)


 HH + eif VV                                      f depends on cone
Phase Cartography
   Experimental Phase Cartography
         --with compensation

          90º



           0º

                                                             5.0
                                                           2.5
         -90º                                             0
                                                               Y
                                                      -2.5
            -5.0    -2.5                            -5.0
                               0     2.5      5.0
                           X
                                              Iris Position
Altepeter et al., Opt. Exp. 13, 8951 (2005)
The problem…
    advantage…
The solution…
                                                     100
                                                    100
                                                    100                                                 400,000
                     Fidelity with Bell State (%)
 Fidelity with Bell State (%)



                                                                                                        350,000
                                                     97.5
                                                    97.5
                                                                                                        300,000
                                                      95
                                                     95
                                                     95
                                                                     Rate                               250,000

                                                    92.5
                                                     92.5                                               200,000

                                                                                                        150,000
                                                     90
                                                      90
                                                     90
                                                                                                        100,000
                                                                Uncompensated
                                                                Uncompensated
                                                    87.5
                                                     87.5
                                                                                                        50,000
                                                                Compensated
                                                                Compensated
                                                     85
                                                     85
                                                      85                                                0
                                                            2
                                                            2
                                                            2    4
                                                                 4
                                                                 4          6
                                                                            6        8
                                                                                     8        10
                                                                                              10   12
                                                                                                   12
                                                                         Iris Diameter (mm)
                                                                      Iris Diameter(mm)
                                                                        Iris Diameter (mm)



Altepeter et al., Opt. Exp. 13, 8951 (2005)
Moore’s law for entanglement
                                                                                  F(-) ~ |HH - |VV
                        The evolution of SPDC polarization-entangleme nt          Re
             10,000,000
                                                                           ?
  )
 -1




              1,000,000
  Reported rate (s




                100,000
                 10,000
                   1,000
                     100
                      10
                        1
                        0
                        1985         1990          1995         2000       2005
                                                                                  Im

Using phase compensation and an optical
recycling technique*, we have observed
polarization-entangled pairs
@ 2,000,000 s-1, with F ~98%!

                                                                                   (Total counting
                                                                                     time = 10 s)
Next main limitation -- detector saturation
                                                                                           *A. White
                     Quantum Tomography
                    of 2-Qubit Polarization States
                                          Detector
                              HWP PBS                         Any 2-qubit tomography
                        QWP                                   requires 16 of these
                                                              measurements.
 Black Box                            This setup allows
  Generates                          measurement of an
  arbitrary*                         arbitrary polarization   Examples:
2-qubit states                        state in each arm.
                                                              Arm 1         Arm 2
                        QWP                                     H             V
                              HWP                               H             R
                                    PBS
                                          Detector              D             D
       HH = 0.507




                                
       HV = 0.345
       VH = 0.110




       RD = 0.234
                                    - Requires 16 measurements
       DH = 0.189
                    Maximum Precise - Gives most likely quantum state
                    Likelihood Density
   16 Precise       Technique Matrix
  Probabilities                           -36 measurements much better
                                                 (e.g., 9 x 4 detectors)
Quantum Tomography Subtleties
With reduced statistical error, systematic effects
   become the dominant source of error:
• Imprecise waveplates
   –   178° phase
   –   Wedged optics
• Accidental coincidences
• Laser intensity drift
• Etc., etc.
We now have available for upload our suite of
   quantum tomography programs (MATLab):
www.physics.uiuc.edu/Research/QI/Photonics/Tomography
        (please email comments, other relevant links)
Bell Tests (more/less than tomography)
•     The density matrix includes full description of
      the quantum system.
•     The measurements needed to estimate the
      density matrix (e.g., HH, HV, HD, VA, etc.)
      are not sufficient to violate Bell’s inequality.
    New source: |Sexpt| = 2.7260 ± 0.0008 216s in 0.8 s
    (SLHV ≤ 2)  |Sexpt| = 2.7392 ± 0.00008 2417s in 2 min

     Optimized    |SQM, max| = 2√2 = 2.828
     Bell test:   |Sexpt| = 2.826 ± 0.005     165s

     Loophole-free htot = hdetectionhcollectionhoptics ≥ ~70%
     Bell test:    hdetector 94  5%??              hcollection
     (in progress) 97%
  New Nonlinear Crystal test - BiBO
             Phase-map from 0.6 mm BiBO (biaxial)

   Background/noise measurements
    (351nm, 25-nm, 10-mm irises)

   BBO (0.6 mm)                BiBO (0.6 mm)
    5400 coin./mW/s             13400 coin./mW/s
    0.75% background            1.5% background

   High quality entanglement obtained in 2-crystal scheme:

    BBO                                BiBO




F = 99.5%                       F = 98.5%
T = 98.4%                       T = 96.9%
S = 3.8%                        S = 6.6%
Quantum
Memories
Quantum Memory: low-loss optical delay line
Applications to scalable quantum logic, quantum “repeaters”,
quantum cryptography, novel quantum communication protocols




Advantagess to 7.9 s delay;
So far: 0.5
• High bandwidth (~5 nm) -- limitedRmirror~ reshaping
                     T ~ 90-7% ( pulse 99.83%)
• Polarization non-decohering
Clean/replace mirrors  Rmirror = 99.99%  T(10s) > 90%
• Adjustable time delay* (10 ns -- 10 s)
Process tomography of 3.9-s system:
• Low loss (with custom mirror coatings)
        >99% pure
• Store multiple k-vectors, complex spatial modes
        mostly sz rotation (43˚); easily corrected w. tilted WP
  *Adjustment is performed by altering the separation and twist angle
 Switchable Low-loss Memory
Switchable cavity:

                             Storage time of n x 1 s


Current Implementation:
              Storage time of n x 27 ns




                                    Brewster- TH=99.4%
                     |H            angle PBS RH=0.5%
                                              TV=0.005%
                               Current loss:
                               3.6%/cycle =
                                  1% (PC)
                                  + 0.5% (PBS)
                                  + 0.2%*4 (mirrors)
                                  + ~1% (mode-matching)

                               Note: already
                 0.5 s        storage time x SPDC > 1!


                               Feasible loss:
                               < 1.5%/cycle =
Cleveland Crystals BBO PC          0.8% (PC)
Driver by BME Bergmann             + 0.2% (PBS)
(“Thorald”):                       + 0.05%*4 (mirrors)
      100 kHz, 6-ns risetime       + ~0.2% (mode-match)
Hyper-Entanglement
  • Photons simultaneously entangled in multiple DOFs:



  • Enlarged Hilbert space:

  • Easy to perform quantum logic between DOFs

  • New capabilities in quantum info. processing
     • full Bell-state analysis
     • “super-duper” dense coding
     • quantum communication with higher alphabets
     • ???

PGK, JMO 44, 2173 (1997)
                          Hyper-entangled state

      Maximally hyper-entangled state:



         F=0.974(1)
         SL=0.039(2)




        T=0.945(2)                                               T=0.943(2)
        SL=0.035(2)                                              SL=0.033(2)




Barreiro et al, PRL 95, 260501 (2005) -- with Univ. Queensland
                 Qubit-qubit-qutrit-qutrit
                    entanglement




        Dimensional Hilbert space!


   • Tomography requires at least
     4x4x9x9 = 1296 measurements

   • Observed 2-qutrit entanglement


         Note:

Barreiro et al, PRL 95, 260501 (2005) -- with Univ. Queensland
       High-Efficiency Single-Photon Detectors
      • Solid State Photomultipliers (SSPMs)
      • Visible Light Photon Counters (VLPCs)

                 Highlights:                               SSPMs
                 • SSPMs originally developed by Rockwell for
                 IR military applications
  VLPCs          • VLPCs are their IR desensitized successors
                 • Very high inferred efficiency (~95%)
                 • Multi-photon detection capability
The Need:             [Takeuchi et al. APL 74, 1063 (1999)]

• High count rate entanglement source
• Single-photon source trigger detector
• Frequency upconversion detector
• Optical Quantum Computing (OQC)
        VLPCs / SSPMs Research Directions
Past performance:
• Extremely high inferred detection efficiency (~95 ± 5%)
• Efficiency limited to < 88% due to in-coupling losses

Our Current Research:
• Gain maximum efficiency and enhanced photon-counting
capabilities by optimizing
   — in-coupling mechanisms  new fibers, custom coatings
   — cryogenics  new dewar designs
   — electronics  new low-noise amplifiers, cryogenic amps

For more info:
     Poster tonight by Radhika “Ria” Rangarajan
 Remaining Issue: Low  at telecom wavelengths (1550 nm)…
Quantum Transduction via
    Up-Conversion
• Quantum Networking
• “Densely” Coded Quantum States
• Single-Photon Detection
   • Quantum Cryptography
• Other Uses“Quantum Ab-King”
  • Low Light Telecommunications
  • IR Astronomy
  • Single Molecule Detection
                 APDs
                Silicon         InGaAs
Efficiency      40-80%          10-20%
Dark Counts     102 s-1         104-105 s-1
After-pulsing   Low             High
Temperature     Room Temp       150 K-250 K
Availability    Off the Shelf   ????
Wavelength      Visible         Infrared
         Experimental Schematic



 = 11.4 m
E = 500 nJ
te = 600 ps
ti = 200 ps
           Up-Conversion Details
dE i     i dQ
     =i              *
               E o E e exp(ikQ z)
 dz      n ic
dE e     e dQ
     =i        E o E i* exp(ikQ z)
 dz      nec
dE o     o dQ
     =i        E i E e exp(-ikQ z)
 dz      n oc



Po (x) sin A Ie z 2
                       (              )   Rabi Oscillation
                            Up-Conversion results
                          16000

                                      2
                          14000



                          12000



                         10000
            Counts (s )
            -1




                                      1
                           8000
                                       2
                                         (1 +  2   )
                           6000



                           4000


       
                           2000
                                      1
                              0
                                  0        1   2         3       4       5        6   7   8   9

                                                             Escort Energy (J)


•      
    Conversion efficiency 99±4%
•   1550-nm single-photon detection efficiency 56±2%
•   Noise level is 10-2 -- 10-3 dark counts/pulse
•   1550-nm extinction level measured up to 96%
       Complex Quantum States
                 1 +  2
   ( 1     +   2 )  ( H +  V            )
a 1,H + b  2 ,H + c 1,V + d  2,V
  

  Can combine with polarization, time-bin, spatial-mode,
   orbital angular momentum, etc., to create very large
   Hilbert spaces as long as conversion is coherent…
                      State Transduction
                                                        14000

                                                          12000

                                                           10000


                          f1550                                                                  f631
             631 nm
                                                                8000

                                                                6000

                                                                4000

                                                                2000

                                                                    0
                                                                    -6.0 -5.0
                                                                                -4.0 -3.1
                                                                                         -2.1 -1.1
                                                                                                   -0.1 0.8
                                                                                                            1.8 2.8
1064 nm
1064 nm                                                                                 Time (ns)
                                                                                              631 nm
                                                                                                                        3.8   4.7   5.7
                                           PPLN
               1550 nm              PPLN
                1550 nm                                         18000

                                                                16000

                                                                14000

                                                                12000
                                             Counts (100 sec)
                                                                10000

                                                                8000


Fringe Visibility ~95%                                          6000

                                                                4000

                                                                2000


 * Tanzilli et al. Nature 437 116 (2005)                           0
                                                                   54.75             55.25         55.75            56.25           56.75
                                                                                                   Tilt (Degrees)
  Summary: Resources and Methods for Quantum Information
• Down-conversion:
   –Very bright sources of entangled states with very high purity
   –Arbitrary states, tunable entanglement & mixedness
• Hyper-Entanglement:
   –Simultaneous in polarization, spatial-mode and energy-time
   –new capabilities in q. info. (e.g., dense-coding, remote
    entanglement preparation)
• Quantum Memory:
   –‘Long-time’ optical storage (up to 7.9 ms)
   –Low-loss switchable system demonstrated (<4% loss/cycle)
• High-efficiency Photon-Counting Detectors:
   –Efficiencies up to 95% in the visible expected, with photon
    number resolution.
• Up-conversion:
   –1550 nm  631nm. 99% conversion achieved. Qubit preserved

				
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