Measurement and Control of Photon Spatial Wave Functions Cody Leary

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1 Measurement and Control of Photon Spatial Wave Functions Cod Lear Oberlin College, April 2012

2 Agenda for toda Measuring the spatial wave function of a single photon Manipulating the wave function of a single photon Imparting a quantum of orbital angular momentum to a photon Interaction between wave functions of two colliding photons

3 What is a photon? A photon is an oscillating electric field (wave) that propagates through space and time A photon makes a photon detector go click! A photon has 4 degrees of freedom (DOFs): Transverse (2-D) photon shape Oscillating electric field amplitude 1.) It oscillates with a certain frequenc (energ) 2.) It oscillates in a certain plane (polarization) 3.) Its intensit (& E-field) in the transverse direction has a certain spatial shape 4.) Its intensit (& E-field) in the transverse direction has a certain spatial shape This talk concerns: The measurement and control of transverse spatial DOFs of photons Photon detecting camera

4 E Transverse spatial modes 1.) Vertical Coffee Bean 2.) Horizontal E Coffee Bean E Intensit= E 2 The electric field of one lobe is out of phase with the other Both modes have either even or odd parit in each dimension: The vertical mode is odd under reflection in The horizontal mode is even under reflection in Phase structure lies at the heart of photon quantum mechanics

5 E Transverse spatial modes 1.) Vertical Coffee Bean 2.) Horizontal E Coffee Bean E Intensit= E 2 Transverse spatial modes are analogous to spherical harmonics in a hdrogen atom Transverse spatial modes are thus the photon's wavefunction

6 E Transverse spatial modes 1.) Vertical Coffee Bean 2.) Horizontal E Coffee Bean E Intensit= E 2 An equal superposition of the vertical and horizontal coffee bean modes results in a new mode: a diagonal coffee bean. = + What I show E TOT, =E Vert, E Hor, What I mean

7 E Transverse spatial modes 1.) Vertical Coffee Bean 2.) Horizontal E Coffee Bean E Intensit= E 2 An equal superposition of the vertical and horizontal coffee bean modes results in a new mode: a diagonal coffee bean. = + How to measure a photon's mode? (vertical, horizontal, diagonal)

8 How not to measure the spatial mode of a single photon A photon counting detector alone cannot measure the transverse spatial mode of a single photon Suppose a vertical photon impinges on such a detector: At this point, the photon could be in either mode: It would take man identical photons to build up the full spatial intensit pattern

9 How to measure the spatial mode of a single photon We need a magic bo that: Accepts an unknown state as input Routes photons to one output Routes photons to a separate output Detector click ields the desired measurement Let's call it a Sorter? S

10 E 1-D parit sorting interferometer BS1 Laser BS2 B A E Parit sorter is based on the superposition principle of the phase of an electric field

11 E 1-D parit sorting interferometer BS1 Laser BS2 B A E

12 E 1-D parit sorting interferometer BS1 Laser BS2 B A E

13 E 1-D parit sorting interferometer BS1 Laser BS2 B A + = 0 E

14 E 1-D parit sorting interferometer BS1 Laser BS2 A = B + = 0 E

15 E 1-D parit sorting interferometer BS1 Laser BS2 B A E Odd modes eit port A

16 1-D parit sorting interferometer

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20 New kid on the block: the donut mode Well-defined orbital angular momentum + = Delaing the phase between the below superposed modes results in evolution of the diagonal coffee bean mode to a donut mode = + = + i No phase dela i=e i 2 =90 o phase dela = cos t + cos t = cos t + sin t

21 Eperimental results Conclusion: the 1-D parit interferometer imparts one quantum of orbital angular momentum to a single photon!

22 Bloch Sphere Arbitrar two-mode superposition represented b sphere Each point on Bloch sphere surface represents distinct state

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24 Solution: optical fiber crushing Data: Margaret Raabe Fiber stress breaks smmetr, imparts relative phase

25 Fiber crushing simulation

26 Eperiment: Theor: Orbital angular momentum ma be deterministicall imparted to a single photon

27 Putting it all together:two photon interference at a beam splitter Discovered b Hong, Ou, and Mandel in 1985 It is commonl thought that photons MUST be indistinguishable

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31 Conclusions: Measurement and Control of Photon Wave Functions Measurement: 1-D parit interferometer sorts photons with even and odd -parit into different ports. Control: Demonstrated phase control between even and odd modes. Imparted a quantum of orbital angular momentum to photons in two was interferometer optical fiber. Collisions : Overlapping photons with nontrivial spatial structure within a 1-D parit interferometer causes their wave functions to interact in surprising was-- interfering photons can be distinguishable!

32 Movie: states that ehibit two-photon interference

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39 2-D parit sorting interferometer (a) Πˆ Πˆ (b) Π = Rˆ o ˆ 180

40 Eperimental results: 2-D parit sorting

41 Controlling a photon's wavefunction with its polarization state orbit -controlled spin rotation spin -controlled orbit rotation The effects occur analogousl for electrons and photons! Independent of mass, charge, magnetic moment, etc.

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43 A brief histor of light and matter Electrons (Matter) Classical Mechanics -Galileo, Brahe, Kepler, Newton Electrons are waves! Quantum (Wave) Mechanics -- Bohr, De Broglie, Heisenberg, Schrodinger Relativit! Relativistic Quantum (Wave) Mechanics -Dirac Particle creation! Quantum Field Theor -Fenman, Tomonaga, Schwinger, Dson Photons (Light) Classical (Ra) Optics -Hero, Ptolem, Sahl, al-hatham, Kepler, Newton Light is a wave! Wave Optics -Hooke, Hugens, Young, Fresnel Relativistic Wave Optics -Mawell, Heaviside, Gibbs, Hertz Quantum Optics -Dirac Relativit! Particle creation! Quantum Electrodnamics

44 A brief histor of light and matter Electrons (Matter) Classical Mechanics -Galileo, Brahe, Kepler, Newton Electrons are waves! Quantum (Wave) Mechanics -- Bohr, De Broglie, Heisenberg, Schrodinger Relativit! Relativistic Quantum (Wave) Mechanics -Dirac Particle creation! Quantum Field Theor -Fenman, Tomonaga, Schwinger, Dson Photons (Light) Classical (Ra) Optics -Hero, Ptolem, Sahl, al-hatham, Kepler, Newton Light is a wave! Wave Optics -Hooke, Hugens, Young, Fresnel Relativistic Wave Optics -Mawell, Heaviside, Gibbs, Hertz Quantum Optics -Dirac Relativit! Particle creation! MY RESEARCH (THEORY AND EXPERIMENT)

45 A brief histor of light and matter Electrons (Matter) Classical Mechanics -Galileo, Brahe, Kepler, Newton Electrons are waves! Quantum (Wave) Mechanics -- Bohr, De Broglie, Heisenberg, Schrodinger Relativit! Relativistic Quantum (Wave) Mechanics -Dirac Particle creation! Quantum Field Theor -Fenman, Tomonaga, Schwinger, Dson Photons (Light) Classical (Ra) Optics -Hero, Ptolem, Sahl, al-hatham, Kepler, Newton Light is a wave! Wave Optics -Hooke, Hugens, Young, Fresnel Relativistic Wave Optics -Mawell, Heaviside, Gibbs, Hertz Quantum Optics -Dirac Relativit! Particle creation! MY RESEARCH (EXPERIMENTAL)