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Dicke Superradiance 01/13 Pavel Cejnar IPNP MFF UK Superradiance 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 laser (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: Quantum optics, Condensed matter + Solid state physics (incl. graphene), Astrophysics, 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 photons 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 Dicke model 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) i1 i1 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 operator, 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 i1 i1 N i1 total quasi-spin 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 Hilbert space 12 3 N bases n N dimA=2 1 2 3 N 0 , 1 , 2 dimF=∞ 12 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* jm [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(m1) m=+½ dt I j2 N 2 j( j1)m(m1) j( j1)(m1)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 ( j1) 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 Phase Transition 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 !.
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