01/13 Pavel Cejnar IPNP MFF UK 02/13 Legacy of Robert Dicke

1946 – Dicke radiometer (development of radar) 1953 – Dicke narrowing (analogous to Mössbauer effect, 1958) 1954 – Dicke superradiance Robert Henry Dicke (1916-97) 1956 – infrared (US patent in 1958, same as Townes & Schawlow in US, and Prokhorov in CCCP) 1965 – prediction (with Peebles, Roll & Wilkinson) of cosmic microwave background (1965 discovered by Penzias & Wilson using Dicke radiometer) 1957-70 – renaissance of gravitation and cosmology (alternative theory to general relativity, anthropic principle…) 03/13 Dicke Superradiance

Cited in: , Condensed + Solid state (incl. graphene), , Nuclear physics, Biophysics + Biology (incl. neurosciences), Engineering … 04/13 Dicke Superradiance

A collection of phenomena named “superradiance”

1) Superradiant flash enhanced non-exponential irradiation of coherent sources 2) Superradiant phase transitions thermal/quantum phase transitions from normal to superradiant phase in interacting matter−field systems 3) Non-hermitian superradiance separation of long- and short-lived states in systems coupled to continuum 4) Zel’dovich-Misner-Unruh superradiance amplification of radiation by rotating black holes …………….. …………….. 05/13 Superradiant flash A sample of N n* two-level atoms M. Gross, S. Haroche, Phys. Rep. 93, 301 (1982) N  n* 1) Independent radiators

t / d N t / n*(t)  Ne I(t)   dt n*(t)   e

t  Probability that n was emitted I  N from a sample of N≈3200 atoms [Raimond et al. 1982] 2) Coherent (collective) radiators  t  N I  N 2 Superradiant pulse in optically pumped HF gas [Skribanowitz et al. 1973] 06/13 cavity Superradiant flash volume V 0 N two-level atoms A schematic model for cavity QED: interaction sample volume V of single-mode radiation with two-level atoms 0 n  single-ω N N photons 1 i  i i  H  0  2  z   b b   x (b  b) i1 i1 N 1 0  0 1     1 i 1 i   0d V0 N D     2    2   • dipole approximation 0 1 cos 1 0 i D,d … dipole , matrix element  0 V V0 phase  ε … electric field intensity  • neglect of the A2 term V0  V  i   i   N N N 1 i i   i i  J  σ H   1    b b  1   1   (b  b)  2 0  2 z  2  2  i1 i1 N i1   total quasi- operators J0 J   J   Conserved quantity    H   J  b b   J  J b  b 2 0 0 N   J  j( j 1) 07/13 Superradiant flash Dicke model

12 3 N bases n  N     dimA=2 1 2 3 N 0 , 1 , 2  dimF=∞

12 3 N  N j  max 2

dimj=2j+1

0 (N even) N!(2 j 1) jmin Rj  1 (N odd) N N  2 ( 2  j 1)!( 2  j)!

R N 1 j 2

  2 j log10 Rj N   2  j n* jm [0,2 j]=number of exc.atoms N=40 j 08/13 j  N  Superradiant flash 2 m=+j n*=2j  J b  J b decay I  j  N Dicke model   m=+j−1    H  0 J0  b b   J   J  b  b  N

Hint

j(m 1) J jm  j( j 1)  m(m 1)  ( j  m)( j  m 1) 2 I  j(m 1) J jm Approximate solution of the decay dynamics:  d 2 2 Pjm   F, j(m 1) Hint F, jm Pjm  F, jm Hint F, j(m 1) Pj(m1) m=+½ dt   I  j2  N 2      j( j1)m(m1)  j( j1)(m1)m m=−½ d d m  m P  ( j  m)( j  m 1)  jm  m   j tanh j(t t0 ) dt m dt  j 2  m2 +j d I  N 2  m dt 1 t  m t N 0 t n*=2 t0 t m=−j+1 n*=1 I  j  N m=−j n*=0 −j 09/13 Superradiant phase transitions  J b  J b Dicke model      H  0 J0  b b   J   J  b  b  m n N  John Daniel Edward Hint M  0 : n,n*  0,0 In this approximation, n* "Jack" Torrance the model conserves  M 1: n,n*  0,1 1,0 (? – ?) the quantity M  n  m  j  M  2 : n,n*  0,2 1,1 2,0  

Assume the resonant case 0  

M=0: H0  j 0 E M=1:   0 2 j  H  ( j1)    Quantum Phase 1   ω N  2 j 0  Transition M=2:  0 2(2 j 1) 0     Superradiant H  ( j 2)   2(2 j 1) 0 4 j  ω 2 phase N   Normal phase  0 4 j 0  −ωj N c ( j) 2 j λ 10/13 Superradiant phase transitions Dicke model extended  [0,1]   ˆ  H  0 J0  b b  b J bJ  [ b J bJ  ] N N N  6, j  2

Thermal QPT QPT QPT   0   0.3  1 normal

superradiant  /  0 0 N Tc  2 2 2artanh  ( N ) /  c ( j)  [ c 2 ] 1 2 j 11/13 Superradiant phase transitions Theory of superradiant phase transitions: Thermal: Y.K. Wang, F.T. Hioe, Phys. Rev. A 7, 831 (1973) K. Hepp, E.H. Lieb, Phys. Rev. A 8, 2517 (1973) Quantum: C. Emary, T. Brandes, Phys. Rev. Lett. 90, 044101 (2003) Experiment F. Dimer et al., Phys. Rev. A 75, 013804 (2007) … proposal K. Baumann et al., Nature 464, 1301 (2010), Phys. Rev. Lett. 107, Realization by means of BEC at T≈50nK in optical cavity 140402 (2011)

Spatial redistribution of BEC leads to undercritical constructive pumping field interference of reflected waves

pumping field of overcritical power 12/13 Non-hermitian superradiance Quasi-bound quantum system with a common set of decay channels. Increasing coupling to continuum leads to seggregation of long-lived (compound) and short-lived (superradiant) resonance states. Applications in nuclear physics (e.g. giant & pygmy resonances…), particle physics (baryon resonances) biophysics (photosynthesis), graphene… Recent reviews: N. Auerbach, V. Zelevinsky, Rep. Prog. Phys. 74, 106301 (2011), I. Rotter, J.P. Bird, Rep. Prog. Phys. 78, 114001 (2015)

A. Volya, V. Zelevinsky, AIP Conf.Proc. 777, 229 (2004) 13/13 ěkuji ! Thank you !