Singular Atom Optics

Some of the earliest experiments done with BECs were creating atom lasers, which provide a convenient analog to understand and extend ideas relating coherent matter (BECs) to coherent light (lasers). Matter wave systems are both intuitively and mathematically similar to optical waves as they are both phase coherent, can be described by a single wavefunction, and are monoenergetic. The field of atom optics has grown to include ray atom optics, wave atom optics, quantum atom optics, and nonlinear atom optics. Experiments include BEC beamsplitters, four wave mixing, matter wave gyroscopes, solitons, superradiance, and more.

Our lab is exploring the connections between angular momentum singular optics and singular BECs. Singular optics is a rich field that deals with the properties and behavior of defects in the phase and/or polarization of light. A hurricane has an eye where the storm is calm; a vortex of light has an “eye” in its center where it is dark (a singularity). Many BEC spin textures and topological excitations of interest include singular spinor components. Singularities involve a complex spatially-dependent phase, so phenomena that affect the phase of a wave, be it in matter or light, are important to understand.

One such phenomenon is the Gouy phase, which, in optics, adds a well-defined phase shift when a laser beam is focused. It has implications and applications in many optical systems. Verifying that there is a Gouy phase in matter waves is important in deepening the connection between BECs and light, studying multimode BEC spin textures and singular atom optics, and in future applications of BECs as quantum technologies. We have developed a new interferometric technique to directly measure the Gouy phase in a BEC, and experiments are underway.

While the Gouy phase in optics dates back to 1890, we are also making singular atom optics analogs to more recent work in singular optics. Full Poincare laser beams contain all possible polarization states in a cross-section of the beam, making them important for polarimetry. This type of beam was first described by Profs. Tom Brown and Miguel Alonso in The Institute of Optics here at UR. The family of Poincare beams is also intrinsically interesting for its propagation properties. This beam consists of, for example, a right hand circularly polarized Gaussian beam, and a left hand circularly polarized Laguerre-Gaussian beam, superimposed coaxially. Its analog is the full Bloch BEC, which contains all possible states on the Bloch sphere.

We have successfully created a full Bloch BEC in the lab using our Raman imprinting technique. The Raman beams couple ground states |F = 2, m_F = 1> and |F = 2, m_F = -1> with Gaussian and Laguerre-Gaussian modes. Half of the population is transferred from |1> to |-1> creating a vortex in the |-1> state. The radius of the vortex is tuned, as the |-1> component must dominate at the edge of the cloud to ensure full coverage of the Bloch sphere. The BEC expands with time, and we verify that full coverage of the Bloch sphere is preserved for the duration of our experiment.

As new ideas are continuously generated in singular optics, we continue to look for ways to apply them to BECs, learning more about both fields in the process. The New York State Center for Complex Light provides an arena for connecting with other researchers in this area.

Learn more

• • Singular atom optics with spinor Bose-Einstein condensates

A. Hansen, J. T. Schultz, and N. P. Bigelow

Optica 3(4) 355-361 (2016).

• • Roadmap on structured light

H. Rubinsztein-Dunlop, et al.

Journal of Optics 19, 013001 (2016).

• • Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate

J. T. Schultz, A. Hansen, J. D. Murphree, M. Jayaseelan, and N. P. Bigelow

Journal of Modern Optics 63, (2016). arXiv

• A Raman Waveplate for Spinor BECs

J. T. Schultz, A. Hansen, and N. P. Bigelow

Optics Letters 39, 4271-4273 (2014). arXiv

• • Full Bloch Bose-Einstein Condensates

A Hansen, JT Schultz, NP Bigelow

Frontiers in Optics, LTu1 (2012)

• • Full Poincare Beams

Amber M. Beckley, Thomas G. Brown, and Miguel A. Alonso

Optics Express 18, 10777 (2010)

• • Experimental proposal for measuring the Gouy phase of matter waves

IG da Paz, PL Saldanha, MC Nemes, JG Peixoto de Faria

New Journal of Physics 13, 125005 (2011)

• • Atomic focusing by quantum fields: Entanglement properties

I.G. da Paz, H.M. Frazão, M.C. Nemes, J.G. Peixoto de Faria

Physics Letters A 378, 1475 (2014)

• Related work

  • • Robert Alfano, Physics, City College of New York

    • Miguel Alonso, The Institute of Optics, University of Rochester

    • Bob Boyd, The Institute of Optics, University of Rochester

    • Tom Brown, The Institute of Optics, University of Rochester

    • Kiko Galvez, Physics, Colgate University

    • Maria Carolina Nemes and Irismar G. da Paz, Physics, Universidade Federal de Minas Gerais (Brazil)

    • Miles Padgett, Physics, University of Glasgow (see video "Light in a Twist" from SPIE)

    • Nirmal K. Viswanathan, Physics, University of Hyderabad

This work has been supported by The National Science Foundation (NSF), The Army Research Office (ARO) of the United States Army Research Laboratory (ARL), The Defense Advanced Research Projects Agency (DARPA) of The United States Department of Defense (DOD), and the NASA-JPL Physical Science Research Program Cold Atom Laboratory (CAL).