Download Bistability and Nonlinear Dynamics in the Dispersive Regime

Cavity QED and Cavity Optomechanics
with a Bose-Einstein Condensate
K. Baumann, T. Bourdel, F. Brennecke, T. Donner, C. Guerlin, M. Köhl, S. Ritter and T. Esslinger
Institute for Quantum Electronics, ETH Zürich, Switzerland
www.quantumoptics.ethz.ch
The system can be described in 2nd quantization, where both the light field
and the matter wave field are characterized by a single mode picture:
• 1D optical lattice consisting of two counterpropagating laser beams
• translation via controlled frequency difference between the two
beams
optical
transport
energy
Spectroscopy of the Strongly Coupled BEC-Cavity System
Optical Transport
bare states
dipole trap
6
σ+
σ−
Photons per 2 ms
5
probe light
single photon
counter
4
3
2
1
0
Cavity parameters
0
20
40
60
80
100
Time (ms)
Probe detuning ∆P (GHz)
5
0
F=1
F’
F=2
F’
−5
−10
Our cavity operates in the strong coupling regime
where the coupling between the cavity and a single
atom dominates all dissipative losses: g0 > γ, κ.
γ
g0
κ
−8
−6
−4
−2
Cavity detuning ∆C/2π (GHz)
0
2
-5
-4
= 2π · 10.4 MHz
= 2π · 3.0 MHz
= 2π · 1.3 MHz
= 3 · 105
= 25 µm
= 176 µm
Probe detuning (GHz)
g0
γ
κ
F
w0
L
σ+
σ−
-3
-2
-1
σ+
σ−
0
0
100'000
200'000
Atom number
300'000
Reference: F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, T. Esslinger
Nature 450, 268 (2007)
400'000
Bistability and Nonlinear Dynamics in the Dispersive Regime
Coherent Dynamics
Photon count rate (MHz)
4
3
2
A B C
1
0
−10
−5
0
5
10
Pump-Cavity detuning (κ)
Effective Potential for the Matterwave Oscillator:
A
6
4
2
0
−10
−5
0
5
10
Time (ms)
B
C
Photon count rate (MHz)
intracavity photon number
Optical Bistability
6
4
2
0
1.2
1.4
1.6
Time (ms)
1.8
While scanning the probe
laser frequency upwards, a
coherent dynamics is triggered due to the non-adiabatic
transition from the lower to
the upper stable branch.
These oscillations can be observed over several ms. The
maximum intracavity photon
number for this trace was ~7.
2
0
0.02
0.01
-2
0.1
0
0.7
0.35
0
80
90
100
0
50 100 150
time τ (µs)
110
120
cavity−pump detuning ∆c (2π MHz)
→ optical bistability below the single photon level!
→ equation of motion of a harmonic oscillator which is
coupled via radiation pressure to the cavity field:
1
cavity
1.05
0.2
0
Reference:
2hk
1.4
0.3
-1
Define
2
cavity
1.75
All atoms are initially in the zeromomentum state. Once light enters the
cavity, a small portion is scattered into
the
states, which gives rise
to the oscillatory behavior of the
system. The picture on the right shows
an absorption image of the atoms after
time of flight where the two higher momentum states are clearly visible.
(zero-momentum state subtracted)
0
2hk
0
0.6
0.5
0.4
0.3
0.2
0.1
0
g(2) (τ)
2
mean intracavity photon number|α|
• dispersive shift of the cavity
resonance due to the BEC:
Oscillation of the BEC-Cavity overlap under free kinetic evolution:
positive scan
negative scan
theory
0.03
with
The BEC wavefunction evolves as a coherent superposition
of the
momentum states:
Measurement of the Steady State Behavior:
0.04
• cavity optical lattice
potential per photon:
Two-Mode Model:
Physical Process:
0.05
Two-Mode Model:
Theoretical description
F. Brennecke, S. Ritter, T. Donner, T.Esslinger ; Science 322, 235 (2008)
S. Ritter, F. Brennecke, K. Baumann, T. Donner, C. Guerlin, T. Esslinger ; APB 95, 213 (2009)