Measurement and Control of a Photon's Spatial Wavefunction

Measurement and Control of a Photon's Spatial Wavefunction Cod Lear The College of Wooster, Januar 2011 Institute of perimental Phsics Optics Division Universit of Warsaw Poland

brief histor of light and matter lectrons (Matter) Classical Mechanics -Galileo, rahe, Kepler, Newton lectrons are waves! Quantum (Wave) Mechanics -- ohr, De roglie, 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 lectrodnamics

Motivation: What I do and wh I do it I develop new was of measuring and controlling the wavefunction (or intensit distribution) of single photons This is worth doing: It allows for direct eperimental probing of the fundamentals of quantum theor (wavefunctions tell ou everthing!) photon's wavefunction carries quantum information (quantum bits) which have practical applications This is fun to do: ll m eperiments ma be done on as tabletop phsics Large group collaboration is not required Undergraduates can (and have!) make crucial contributions

What is a photon? photon is an oscillating electric field (wave) that propagates through space and time photon makes a photon detector go click! 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 (& -field) in the transverse direction has a certain spatial shape 4.) Its intensit (& -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

Transverse spatial modes 1.) Vertical Coffee ean 2.) Horizontal Coffee ean Intensit= 2 The electric field of one lobe is out of phase with the other oth 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

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

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

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

How to measure the spatial mode of a single photon We need a magic bo that: ccepts 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

1-D parit sorting interferometer Laser Parit sorter is based on the superposition principle of the phase of an electric field

1-D parit sorting interferometer Laser

1-D parit sorting interferometer Laser + = 0

1-D parit sorting interferometer Laser = + = 0

1-D parit sorting interferometer Laser Odd modes eit port

1-D parit sorting interferometer Laser ven modes eit port

1-D parit sorting interferometer Laser = + diagonal coffee bean input mode is split into its corresponding vertical and horizontal components.

perimental results perimental Setup Laser Camera

perimental results perimental Setup With glass slide inserted Laser Glass Slide Camera Output mode is controlled b tilting the glass slide

New kid on the block: the donut mode Well-defined orbital angular momentum (2-D parit) + = 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

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

Intermission The 1-D parit interferometer is the simplest of several devices I designed and built along with undergraduates Working under m direction, an undergraduate summer student (Zach ond) built and tested this sorter over 10 weeks, taking the data just shown and presenting it at a national undergraduate smposium. nother undergraduate (shleigh aumgardner) is a coauthor on a paper we published in the international journal Optics press Net up: proposed senior I.S. eperiment Conclude with an broader view of m research

Quantum eperiment: single photon Single Photon input = + Put one diagonal photon in the input port, and it must CHOOS whether to be in a vertical or horizontal mode at the output Global measurement with local detectors! This eperiment has never been done Onl one detector can click This device measures parit of single photons!

roader view of m research Measuring a photon's wavefunction (1-D parit sorter) Imparting orbital angular momentum to a single photon Measuring a photon's wavefunction (2-D parit sorter) Controlling a photon's wavefunction with its own polarization state in optical fibers Direct analogies between the dnamics of photons and electrons in clindrical geometries Hdrogen atom for photons?

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

perimental results: 2-D parit sorting

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.

Conclusions Just like electrons, photons have wave functions (transverse spatial modes) I have learned to measure and control them directl: 1-D Parit 2-D Parit nd indirectl: spin-controlled wavefunction rotation Used to transfer quantum info between DOFs Together, the above methods allow (in principle) for universal quantum information processing lectrons and photons evolve identicall in clinders What about spherical smmetr? (Hdrogen atom!) Trap photons in glass spheres- store quantum info!

Spin-orbit interaction eperiment 3 Mode Fiber SM Fiber Laser Glass plates To Polarization nalzer Fiber Crusher 2-D Sorter Odd Port ven Port To 1-D Sorter Test Fiber

Quantum eperiment: two photons Single Photon input 1 2 Single Photon input Put two photons in different input ports, and ou get out ITHR two vertical photons OR two horizontal ones, but NVR one of each! 1 2 This eperiment has never been done