Long phase coherence times in the microcavity polariton condensate

1
Long phase coherence times in the microcavity
polariton condensate

• A. P. D. Love, D. N. Krizhanovskii, D. M.
  Whittaker, D. Sanvitto, M. S. Skolnick, P. R.
  Eastham, R. André and Le Si Dang
• 1 Department of Physics and Astronomy, University
  of Sheffield, Sheffield S3 7RH, UK
• 2 Dep. Fisica de Materiales, Universidad Autonoma
  de Madrid, 28049 Madrid, Spain
• 3 Condensed Matter Theory Group, Imperial
  College, London SW7 2HZ, UK
• 4 Institut Néel, CNRS and Université J. Fourier,
  38042 Grenoble France

In press - Phys. Rev. Lett. (Aug 2008)
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Outline

• Background
• Microcavity polaritons
• Polariton condensation
• Temporal Coherence
• Noise free excitation conditions
• Long 1st and 2nd order coherence times
• Coexisting condensates
• BEC, OPO generality?
• Summary

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Semiconductor Microcavity

• Strong coupling
• Low mass (low density of states)
• Ideal system to study interacting BEC
• Large Rabi splitting O26 meV for CdTe based
  microcavities used. 16 QWs

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Non-resonant
High density state
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Emission spectra non resonant excitation
Below Threshold
Clear threshold behaviour for all modes
Blue-shift 0.5meV
Above Threshold

• 5-10µeV linewidth with CW noise free diode laser
  (at 1.81eV)
• 0.3meV previously reported for multimode laser
  excitation (Kasprzak et al, Nature (2006),
  0.55meV Balili, Snoke Science 2007)
• 2 orders of magnitude reduction in linewidth
  reveals new physics

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Comparison of BEC spectra excited with multimode
and noise free diode lasers
Multimode laser Linewidth of BEC emission 1 meV
Noise free diode laser BEC emission consists of
sharp Peaks, linewidth 10 meV From coherence
time
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Real Space Images

• Size of laser spot 15 µm
• 3 modes the same as on previous slide
• Above threshold
• Size of the modes 10-15 µm
• Separation between modes 2 µm. Strong
  overlapping
• Localisation due to fluctuations in photonic
  potential
• Coexistence of multiple condensates

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First Order Coherence
Limited by interactions
Occupancy

• Above threshold g(1) function decays on a time
  scale of 120-150 ps (5-10?eV), 30-50 times
  slower than with multimode laser
• g(1) has Gaussian lineshape
• Initial increase of coherence time with occupancy
  as in laser
• Coherence time increases as function of number of
  particles in the condensate and then saturates at
  120-150 ps. Signature of interactions

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Second Order Coherence

• Below threshold
• g(2)(0) 2 with (detector limited)
• Above threshold
• g(2) decays on timescale 100ps gt resolution time
• g(2)(0) 1.1 (also see Kasprzak et al, PRL
  (2008)) close to value of 1 for coherent state

0
Delay Time t (ns)
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g(1) and g(2) analysis

• For an isolated, equilibrium state g(1) and g(2)
  given by
• Using measured g(2)(0) 1.1, gives g(1) decay
  time of 220ps - close to experimental value of
  150ps
• Predicted decay is Gaussian agreeing with
  experiment
• Consistency between g(1) and g(2)

Mean number of particles
Blueshift
Variance
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• But not true equilibrium system
• Dynamic equilibrium is maintained by stimulated
  scattering, which offsets the cavity losses
  (2psec timescale)
• The g(2) decay time of 100psec sets timescale of
  interactions within condensate
• Of order of g(1) decay time of 200psec hence
  condensate has coherence properties of
  equilibrium system
• Quantum optical theory, Th-A3d2 (D M Whittaker)

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Why are long coherence times now found

• Use of noise free diode laser (noise free on
  0.1-1ns timescale)
• Eliminates large broadening mechanism with
  multimode laser
• Multimode laser intensity fluctuations of 20
  on ns timescale
• Lead to fluctuations in exciton density.
• Blueshift of 1meV from below to above threshold
  due to interactions
• For a 1meV blueshift 20 fluctuations correspond
  to 0.2meV extrinsic broadening corresponding
  to 10ps coherence time
• Such fluctuations have obscured the true
  coherence properties in previous work

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Resonant
Non-resonant
OPO
Same coherence properties??
High density state
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Variation of OPO Coherence Time With Occupancy of
State
PRL 97, 097402 (2006)
Theory

• Initial rapid increase, followed by near
  saturation at 500psec
• Very similar to BEC
• Property of interactions and occupancy, very
  similar in two cases

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Summary

• Long coherence times reported for non-resonantly
  excited CdTe based microcavities
• Noise free laser essential for excitation
• Co-existing condensates
• Interactions limit coherence times
• The polariton condensate exhibits properties
  characteristic of an equilibrium BEC, even though
  it is subject to gain and loss with its
  environment
• Coherence properties very similar to optical
  parametric oscillator. Coherence times property
  of interactions and occupancy which are both very
  similar in BEC and OPO

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GaAs OPO Spectrally Resolved Images above
threshold
PRL 97, 097402 (2006)
Photonic disorder again important
Decreasing energy, less blue shift
Below threshold
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Experimental Setup - g(1) Measurement
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Experimental Setup - g(2) Measurement
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Polariton Condensation in CdTe

• We use noise free diode laser
• Allows true condensate coherence to be accessed

Relaxation
Kasprzak et al, Nature (2006)
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Theoretical Model

• From the measured g(2)(0) of 1.1, the decay of
  g(2) is predicted to be 100ps, in very good
  agreement with experiment
• g(1) has a Gaussian shape with a decay time of
  220ps
• Polariton condensate can behave like an
  equilibrium BEC on timescales much longer than
  the cavity lifetime
• Further details of theory presented in talk
  Th-A3d2 (David Whittaker)