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BEYOND LINEAR OPTICS: ZENO GATES AND PHOTON HOLES

2. OUTLINE. Motivation

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BEYOND LINEAR OPTICS: ZENO GATES AND PHOTON HOLES

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    1. BEYOND LINEAR OPTICS: ZENO GATES AND PHOTON HOLES Jim Franson Johns Hopkins University

    2. 2

    3. MOTIVATION

    4. 4 MOTIVATION FOR ZENO GATES There has been considerable progress in LOQC by many groups Quantum logic including CNOT gates Single-photon sources and detectors Small scale circuits Quantum error correction Cluster states There are several ways to deal with the failure events: The failure rate can be made arbitrarily small by using a large number of ancilla Cluster states The failure events can be eliminated using the quantum Zeno effect A random event can be suppressed by frequent observations to see if it has occurred “A watched pot never boils”

    5. 5 QUANTUM ZENO EFFECT Frequent measurements can inhibit an error

    6. 6 ZENO GATES Our CNOT gate works correctly if one photon exits in each mode All failure events are due to two photons leaving in the same path These failure events can be suppressed by frequent observations to determine if two photons are present in the same output path

    7. 7 IMPLEMENTATION OF ZENO GATES The Zeno effect requires a continuous process The beam splitters are replaced with coupled fiber devices The emission of two photons into the same fiber can be inhibited by frequent measurements to see if two photons are there This is equivalent to adding atoms to the fibers that can absorb two photons but not one The atoms “watch” for the presence of two photons

    8. 8 SUPPRESSION OF ERRORS USING THE ZENO EFFECT We assumed that N equally-spaced measurements were made to determine whether or not two photons were in the same fiber As expected from the quantum Zeno effect, the emission of two photons into the same fiber was suppressed for large N The same results were obtained using two-photon absorption

    9. 9 TWO-PHOTON ABSORPTION AND CAVITIES The required two-photon absorption can be enhanced using a resonant cavity The energy of a single photon is concentrated in a small region Several different cavity designs are being investigated Single-photon absorption can be reduced using electromagnetically induced transparency (EIT) Without any laser beams (quant-ph/0603044)

    10. ENTANGLED PHOTON HOLES

    11. 11 OUTLINE Concept of entangled photon holes Somewhat analogous to holes of semiconductor theory Can be generated using two-photon absorption Violations of Bell’s inequality Requires single-photon detectors Macroscopic effects Can be observed using classical detectors Nonclassical reduction in the two-photon absorption rate Could be a concern in Zeno gates

    12. GENERATION OF ENTANGLED PHOTON HOLES

    13. 13 REVIEW OF TWO-PHOTON ABSORPTION A three-level atom is assumed to be off resonance from photon 1 A virtual transition can occur in which photon 1 is absorbed first Followed by photon 2 For large detunings, the two photons are absorbed at very nearly the same time

    14. 14 COMPARISON WITH DOWN-CONVERSION In parametric down-conversion, two photons are generated at the same time but that time is uncertain (energy-time entanglement) With a coherent superposition of those times In two-photon absorption, two photons are annihilated at the same time With a coherent superposition of those times The dips in the probability amplitude can be viewed as holes in an otherwise constant background Somewhat analogous to the holes of semiconductor theory

    15. VIOLATIONS OF BELL’S INEQUALITY

    16. 16 FIRST CONSIDER PAIRS OF PHOTONS FROM DOWN-CONVERSION Suppose the two photons travel in opposite directions to two interferometers If we only accept events in which the photons arrive at the same time, there are two possibilities They both took the long path ( ) or the short paths ( ) There is no contribution from or Interference between and gives a coincidence rate proportional to Violates Bell’s inequality

    17. 17 VIOLATION OF BELL’S INEQUALITY USING ENTANGLED PHOTON HOLES Once again, consider two distant interferometers and assume the dips go to zero Now there is no contribution from or The photons are never emitted at the same time Interference between and now give a coincidence rate proportional to Also violates Bell’s inequality

    18. MACROSCOPIC EFFECTS OF ENTANGLED PHOTON HOLES

    19. 19 EFFECTS OF ENTANGLED PHOTON HOLES A classical state of light is assumed to be incident on a two-photon absorbing medium As the photons propagate through the medium, the magnitude of the dips in the probability amplitude will increase At some point, there should be no probability amplitude for two photons to be in the same location So the rate of two-photon absorption should go to zero But the probability amplitude for two photons to be found in different locations will be nearly unaffected Thus the two-photon absorption should stop when the total probability of absorption is still small

    20. 20 TWO-PHOTON ABSORPTION CALCULATIONS Earlier calculations used Semiclassical theory or One or two second-quantized modes or A continuum of second-quantized modes to lowest order in perturbation theory The effects of interest here require a multi-mode calculation to all orders In the absence of an analytic solution, Schrodinger’s equation was integrated numerically For two gaussian wave packets as input

    21. 21 HAMILTONIAN Each photon was limited to k vectors (periodic B.C.) There are a total of states in the state vector states corresponding to two photons with and states corresponding to a single photon and the atom in the first excited state One additional state with the atom in the upper level The Hamiltonian in this basis is

    22. 22 NUMERICAL INTEGRATION With this Hamiltonian, Schrodinger’s equation corresponds to a set of coupled differential equations The Hamiltonian contains more than terms This set of differential equations was integrated numerically using Mathematica The execution time did scale as The equations could be integrated in four hours for This was used as the baseline A subset of the calculations were repeated using Gave the same results

    23. 23 INITIAL STATE The single-photon intensity was calculated by tracing over the photon 2 components The probability of detecting two photons separated by a distance s was calculated as usual using

    24. 24 AFTER PROPAGATION THROUGH 5 mm The photon wave packets were propagated through a distance of 5 mm The single-photon intensity was nearly the same The two-photon detection probability shows a small dip as expected

    25. 25 PROBABILITY OF REMAINING IN THE INITIAL STATE The wave packets were propagated through atoms The probability of remaining in the initial state was calculated It can be seen that the two-photon absorption rate decreases The probability reaches a plateau after ~ 20 atoms

    26. 26 COMPARISON OF THREE CASES Photons in same direction Semiclassical results Photons in opposite direction

    27. 27 SUMMARY OF ENTANGLED PHOTON HOLES Entangled photon holes are somewhat analogous to the holes of semiconductor theory The analogy is obviously limited since photons are bosons The “background” corresponds to small probability amplitudes vs unity for fermions below the Fermi level Entangled photon holes can violate Bell’s inequality using single-photon detectors Entangled photon holes can have macroscopic effects on two-photon absorption Can be measured using a classical source and detector Entangled photon holes can also be generated using down-conversion techniques

    28. EIT WITHOUT ANY LASER BEAMS

    29. 29 CONVENTIONAL EIT A beam on resonance with atomic level will be strongly absorbed Due to scattering into A strong laser beam resonant with and will split the original state into dressed states and There are now two ways (Feynman diagrams) to reach state Via (negative detuning) Via (positive detuning) These two probability amplitudes cancel each other The scattering is completely eliminated We would like to avoid laser beams (for single photons)

    30. 30 EIT WITHOUT LASER BEAMS Instead of splitting an energy level, we tune between two of the resonant modes of a cavity Photons in a wave guide are coupled to the ring resonator but not directly to the atoms The probability amplitudes for scattering by the atoms cancel out as before

    31. 31 ENHANCED TWO-PHOTON ABSORPTION WITH NO SINGLE-PHOTON SCATTERING Two-photon absorption can still occur via other pairs of intermediate states We estimate that the two-photon absorption can be four orders of magnitude larger than the single-photon absorption Ideal for Zeno gates (quant-ph/0603044)

    32. SUMMARY

    33. 33 SUMMARY The failure modes of LOQC can be suppressed using the Zeno effect Requires strong two-photon absorption Two-photon absorption can be enhanced using small cavities and EIT without laser beams Entangled photon holes are somewhat analogous to the holes of semiconductor theory Bell’s inequality can be violated using single-photon detectors Macroscopic effects of entanglement can be observed using classical input states and classical detectors

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