Prospects for a superradiant laser M. Holland murray.holland@colorado.edu Dominic Meiser Jun Ye Kioloa Workshop D. Meiser, Jun Ye, D. Carlson, and MH, PRL 102, 163601 (2009). D. Meiser and MH, PRA 81, 033847 (2010). D. Meiser and MH, PRA 81, 063827 (2010). M. Holland () Superradiant laser Kioloa Workshop 1 / 21
Overview Conventional laser: What do we mean by a laser? The basic idea: Superradiance in steady-state Application with 87 Sr: Making a stable coherent light source M. Holland () Superradiant laser Kioloa Workshop 2 / 21
Conventional laser Cavity, internal ratchet, pumping, output coupling,... Brightness; many photons per mode Coherent; long coherence length, coherence time M. Holland () Superradiant laser Kioloa Workshop 3 / 21
Schawlow-Townes Linewidth Noise added to circulating field Amplitude fluctuations damped Phase fluctuations random walk M. Holland () Superradiant laser Kioloa Workshop 4 / 21
Where are the atom dynamics? Γ κ g Atomic decay rate Cavity decay rate Atom-cavity coupling Normal laser: atomic relaxation rates much faster than field relaxation rates (left case) Cavity dynamics completely contained in bandwidth of atom Adiabatic elimination of the atoms: Γ κ, g M. Holland () Superradiant laser Kioloa Workshop 5 / 21
Basic idea: reverse the roles of atoms and cavity n cavity photon occupancy: importance of stimulated emission N 1 Ĵ+ Ĵ, with N the atom number: importance of superradiant emission N 4 N 1 J J Atomic collectivity 1 Superradiance Crossover this talk Laser Subradiance 1 n Field collectivity M. Holland () Superradiant laser Kioloa Workshop 6 / 21
Superradiance: most simple example Two atoms, two internal states and Decay operator J = ( ) Γ σ (1) + σ(2) Emission rate ψ J + J ψ Four basic possibilities for ψ, emission rate 2Γ 1 ( ) 2 +, emission rate 2Γ, superradiance ( 1 ) 2, emission rate 0, subradiance, emission rate 0 Constructive or destructive quantum interference M. Holland () Superradiant laser Kioloa Workshop 7 / 21
How does optical atomic clock work? (theorist s version) Frequency standard: Ultra-narrow atomic transition (e.g. in Sr, 1 mhz) Counter: Ultra-stable laser ( 1 Hz) + frequency comb Bottleneck: Interrogation laser M. Holland () Superradiant laser Kioloa Workshop 8 / 21
Circumventing reference cavity Question Is it possible to extract radiation directly from the atoms (spontaneous emission)? Problem: Extremely feeble P NΓ ω 10 16 W (in 4π) Threshold of usefulness: 10 14 W M. Holland () Superradiant laser Kioloa Workshop 9 / 21
Our proposal Use collective emission inside a cavity to gain another factor of N P N 2 Γ ω 10 10 W (in one mode) Key message: Forced to study cavity QED with extremely small dipole moment. M. Holland () Superradiant laser Kioloa Workshop 10 / 21
Why group II atoms? Two-electron system Narrow intercombination lines Small dipole moment ( 10 5 ea 0 ) 2 1 S 0 2 1 P 1 1 1 S 0 singlet triplet dipole forbidden + 2 3 P 2 3 2 P 2 3 1 P 0 metastable Consequences: Weak coupling to cavity field Long atomic coherence times (> 1s) M. Holland () Superradiant laser Kioloa Workshop 11 / 21
Model Two level atoms, in vibrational ground state (Lamb-Dicke regime) Single mode quantized light field Collective atom-field interaction Cavity decay (outcoupling) Non-collective decay processes (spontaneous emission, repumping, inhomogeneous broadening) γ ω a Trapping Cooling Repumping κ M. Holland () Superradiant laser Kioloa Workshop 12 / 21
Mathematical description Coherent part Ĥ = ω a 2 N ˆσ j z + ω câ â + Ω 2 j=1 â N ˆσ j j=1 + â N ˆσ j + j=1. Completely collective Ĥ = ω a Ŝ z + ω c â â + Ω 2 ( â Ŝ + âŝ +). M. Holland () Superradiant laser Kioloa Workshop 13 / 21
Mathematical description, dissipative processes Von Neumann equation: Liouvillian: d dt ˆρ = 1 i [Ĥ, ˆρ] + L[ˆρ] L[ρ] = L cavity [ρ] + L spont. [ρ] + L inhom. [ρ] + L repump [ρ] For instance spontaneous emission: L spont [ˆρ] = Γ 2 N j=1 ( ˆσ + j ˆσ j ˆρ + ˆρˆσ + j ˆσ j 2ˆσ j ˆρˆσ + j ), Decay processes address individual atoms (non-collective) M. Holland () Superradiant laser Kioloa Workshop 14 / 21
Numbers parameter symbol value homogeneous linewidth Γ 0.01 s 1 atom-field coupling Ω 37.0 s 1 inhomogeneous lifetime T 2 1 s repumping rate w 10 3 10 4 s 1 cavity decay rate κ 9.4 10 5 s 1 cavity finesse F 10 6 number of atoms N 10 3 10 6 cooperativity parameter C 0.14 Take home message: Cavity relaxation rate much faster than atomic relaxation rates C = Ω 2 /(Γκ) (single atom cooperativity parameter) M. Holland () Superradiant laser Kioloa Workshop 15 / 21
Bad cavity laser Normal laser: atomic relaxation rates much faster than field relaxation rates Here: atomic dynamics completely contained in bandwidth of cavity M. Holland () Superradiant laser Kioloa Workshop 16 / 21
Intensity Threshold: w Γ Above threshold: sharp increase of emitted power Second threshold (w max NCΓ): Non-collective emission Max. power: P max = N(NCΓ ω a) 8 Critical particle number: N crit. = 4 CΓT 2 P Watt 10 13 10 15 10 17 N 10 6 10 5 10 4 0.01 1 100 10 4 w s 1 Γ w max 10 21 10 3 10 3 10 2 10 1 1 10 1 10 2 10 3 w s 1 10 12 10 15 10 18 P W M. Holland () Superradiant laser Kioloa Workshop 17 / 21
Spectra Use quantum regression theorem to find â (t)â(0) Spectrum: S(ω) = dte iωt â (t)â(0) S Ω 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.5 0.0 0.5 1.0 10 6 Ω s 1 Minimum linewidth ν = 4CΓ Much smaller than Schawlow-Townes linewidth N 10 5 10 4 Γ T 2 1 w max 10 3 10 2 10 1 1 10 1 10 2 Ν laser s 1 10 3 10 3 10 1 10 1 10 3 w s 1 M. Holland () Superradiant laser Kioloa Workshop 18 / 21
Big picture question: Isn t this just a laser? M. Holland () Superradiant laser Kioloa Workshop 19 / 21
LASER vs. Superradiance Atoms: microscopic, independent Field: macroscopic, coherent Enhancement of emission due to stimulation Coherence due to final state Atoms: macroscopic, coherent Field: microscopic Enhancement of emission due to interference in initial state Coherence due to initial state M. Holland () Superradiant laser Kioloa Workshop 20 / 21
Summary: physical realizations Lattice clocks Extremely well controlled environment Small decoherence rates Raman transitions between magnetic sublevels in Alkali-atoms Powerful laser cooling schemes, evaporative cooling Flexible level schemes (tunable coupling strengths, decay rates,...) Several cavity QED experiments in existence Trapped ions NV-centers in diamond In crystal easy to have many of them Large inhomogeneous broadening Nuclear transitions in 229 Th Very insensitive to environment M. Holland () Superradiant laser Kioloa Workshop 21 / 21