• 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
