• The Electric field in the condensate with susceptibility is governed by the Helmholtz equation:

• The light backscattered by the atoms interferes with each pump beam to create a dipole potential:

• The condensate wavefunction is modeled with the GPE:

Spontaneous Crystallization of Light and MatterIvana Dimitrova, Jesse Amato-Grill, Niklas Jepsen, William Lunden, Wolfgang Ketterle

One-Sided Pump Two-Sided Pump

t<tR

t>tR

Regimes of Light-Matter Interactions

TOF Patterns Back-reflected Light

Kapitza-Dirac

Superradiance

Spontaneous Crystallization

S. Ostermann, F. Piazza, and H. Ritsch. Phys. Rev. X 6, 021026. 2016.

• Initially atoms form a standing density wave (symmetric peaks in TOF)

• Persists for ~tR due to Fourier broadening of the pump beam; later suppressed by energy conservation

• Atoms form a density wave moving with , ,etc (with one-sided satellite peaks in TOF)

• Threshold effect; collective emission competes with decoherence of scattered mode as modeled by:

• Critical Rayleigh scattering rate:

• Atoms form a stationary density pattern• Threshold is similar to Superradiance, but much

higher power for elongated geometries:

• At Rcrit, potential depth depends on detuning

• Symmetric peaks in TOF that oscillate in time after a quench

• The phase of the resulting density pattern w.r.t. the condensate is spontaneously chosen

• The spectrum develops a phonon gap at high energies:

TheorySetup

S. Ostermann, F. Piazza, and H. Ritsch. Phys. Rev. X 6, 021026. 2016.

S. Ostermann, F. Piazza, and H. Ritsch. Phys. Rev. X 6, 021026. 2016.

S. Ostermann, F. Piazza, and H. Ritsch. Phys. Rev. X 6, 021026. 2016.Dominik Schneble, Yoshio Torii, Micah Boyd, Erik W. Streed, David E. Pritchard, Wolfgang Ketterle. Science, Vol 300, 475-578. 2003.

S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, J. Stenger, D. E. Pritchard, W. Ketterle. Science, Vol 285, 571-574. 1999.

• For the case of single beam pumping, we observe the satellites grow and then decay due to Rayleigh heating

• For the double-sided pump, we observe oscillations (similar to KD oscillations in an optical lattice)

• Back-reflected light from the crystal provides a real-time, non-destructive measurement of crystal dynamics

• While we expect light scattered from an ordinary condensate to be recoil-shifted in frequency, we expect light reflected by the crystal to have no frequency shift

• The intensity and frequency of reflected light from each beam can be independently monitored via homodyne detection