Non-exponential decay of Feshbach molecules Saverio Pascazio - PowerPoint PPT Presentation

Non-exponential decay of Feshbach molecules Saverio Pascazio Dipartimento di Fisica and INFN Bari, Italy in collaboration with P . Facchi and F . Pepe CUAS, Padova, 27 September 2013

preliminaries: the survival probability of a decaying system survival 1 − t 2 (Zeno) probability τ 2 Z 1 (exponential) Ze − γ t (power) t − α time

in QM and QFT survival probability P ( t ) = Z exp ( − γ t ) + additional contributions second order in wave function coupling constant renormalization exponential decay modified at short (Zeno effect) and long times (power law)

in QM and QFT survival probability OBSERVE in EXPT? P ( t ) = Z exp ( − γ t ) + additional contributions second order in wave function coupling constant renormalization exponential decay modified at short (Zeno effect) and long times (power law)

von Neumann,1932 History Beskow and Nilsson,1967 Khalfin 1968 Friedman 1972 Misra and Sudarshan, 1977

von Neumann,1932 History Beskow and Nilsson,1967 Khalfin 1968 Friedman 1972 Misra and Sudarshan, 1977 (main) Experiments (Cook 1988) Itano, Heinzen, Bollinger, and Wineland 1990 Nagels, Hermans, and Chapovsky 1997 Wunderlich, Balzer, and Toschek, 2001 Fischer, Gutierrez-Medina, Raizen, 2001 Streed, Mun, Boyd, Campbell, Medley, Ketterle, Pritchard, 2006 Bernu, Sayrin, Kuhr, Dotsenko, Brune, Raimond, Haroche 2008

von Neumann,1932 History Beskow and Nilsson,1967 Khalfin 1968 Friedman 1972 Misra and Sudarshan, 1977 (main) Experiments (Cook 1988) Itano, Heinzen, Bollinger, and Wineland 1990 Nagels, Hermans, and Chapovsky 1997 Wunderlich, Balzer, and Toschek, 2001 Fischer, Gutierrez-Medina, Raizen, 2001 Streed, Mun, Boyd, Campbell, Medley, Ketterle, Pritchard, 2006 Bernu, Sayrin, Kuhr, Dotsenko, Brune, Raimond, Haroche 2008 Theory and interesting Mathematics

experiment on “unstable” system Wilkinson, Bharucha, Fischer, Madison, Niu, Sundaram, and Raizen, Nature 1997

 a more recent experiment                                                  

 a more recent experiment  (a) 1   0.9  0.8 P(t), P Z (t)       0.7           0.6    0.5 0 1 2 3 4 5      t / T B 1 (b) 0.8       0.7 P(t), P Z (t)       0.6           0.5 0.4 0.3 0.2 0.0 0.5 1.0 1.5 2.0 2.5 t / T B Lörch, Pepe, Lignier, Ciampini, Mannella, Morsch, Arimondo, Facchi, Florio, Pascazio and Wimberger, PRA 2012

 a more recent experiment  Z (a) 1   0.9  0.8 P(t), P Z (t)       0.7           0.6    0.5 0 1 2 3 4 5      t / T B Z 1 (b) 0.8       0.7 P(t), P Z (t)       0.6           0.5 0.4 wfr Z: Facchi, Nakazato and P ., PRL 2001 0.3 0.2 0.0 0.5 1.0 1.5 2.0 2.5 t / T B Lörch, Pepe, Lignier, Ciampini, Mannella, Morsch, Arimondo, Facchi, Florio, Pascazio and Wimberger, PRA 2012

the ideas to be discussed today stable vs unstable non exponential decay wave function renormalization BEC-BCS

Hamiltonian H = H 0 + H AM + H F ✓ q 2 p 2 ◆ X X X 2 mc † b † H 0 = p, σ c p, σ + 4 m + E B q b q p q σ = " , # ⇣ ⌘ X G ( p ) b † H AM = K c � p + K/ 2 , # c p + K/ 2 , " + h . c . K,p X U ( p, p 0 ) c † p + q/ 2 , " c † H F = � p + q/ 2 , # c � p + q/ 2 , # c p + q/ 2 , " pp 0 q G ( p ) = h ψ M ,K | H int | K/ 2 + p " , K/ 2 � p #i

c † Hamiltonian | ψ M ,K i = b † K | 0 i c † H = H 0 + H AM + H F ✓ q 2 p 2 ◆ X X X 2 mc † b † H 0 = p, σ c p, σ + 4 m + E B q b q p q σ = " , # ⇣ ⌘ X G ( p ) b † H AM = K c � p + K/ 2 , # c p + K/ 2 , " + h . c . K,p X U ( p, p 0 ) c † p + q/ 2 , " c † H F = � p + q/ 2 , # c � p + q/ 2 , # c p + q/ 2 , " pp 0 q G ( p ) = h ψ M ,K | H int | K/ 2 + p " , K/ 2 � p #i

| ψ M , 0 i = b † 0 | 0 i initial state ! | Ψ 0 i = ( b † 0 ) N p | 0 i N ! focus on s -wave Feshbach resonance of 6 Li ( m ' 10 − 25 Kg) at B = 543 . 25 G

atom-molecule interaction c H r L 8000 6000 4000 r max 2000 100 r @ a o D 20 40 60 80 - 2000 - 4000

survival amplitude and propagator self-energy function and spectral function

second Riemann sheet E I ω 0 E II pole

second Riemann sheet E I ω 0 E II pole Im E pole B = B 1 = B res + 2.64 â 10 - 5 G S III H E L B = B res Re E pole S II H E L

E so that I ω 0 II E pole due to cut

lifetime g @ s - 1 D 2.5 â 10 5 2.0 â 10 5 1.5 â 10 5 4 â 10 3 1.0 â 10 5 2 â 10 3 0.5 â 10 5 1 â 10 - 4 B 1 - B res 0.5 B - B res @ G D 0.1 0.2 0.3 0.4

wave function renormalization H» Z »L 2 - 1 3 â 10 - 2 2 â 10 - 2 1 â 10 - 2 B - B res @ G D 0.2 â 10 - 2 0.4 â 10 - 2 0.6 â 10 - 2 0.8 â 10 - 2 1.0 â 10 - 2

wave function renormalization H» Z »L 2 - 1 3 â 10 - 2 !! 2 â 10 - 2 1 â 10 - 2 B - B res @ G D 0.2 â 10 - 2 0.4 â 10 - 2 0.6 â 10 - 2 0.8 â 10 - 2 1.0 â 10 - 2

examples of survival probability P H t L P H t L P H t L - e -g t 1.0 P H t L - e -g t 1.0 0.01 0.02 t t 0.8 1 â 10 - 4 2 â 10 - 4 0.8 2 â 10 - 5 4 â 10 - 5 - 0.05 0.6 0.6 - 0.03 - 0.10 0.4 0.4 0.2 0.2 t t 1 â 10 - 5 2 â 10 - 5 3 â 10 - 5 4 â 10 - 5 5 â 10 - 5 0.5 â 10 - 4 1.0 â 10 - 4 1.5 â 10 - 4 2.0 â 10 - 4 2.5 â 10 - 4 (a) B − B res = 1 . 2 × 10 − 2 G (b) B − B res = 9 . 2 × 10 − 4 G

examples of survival probability P H t L P H t L P H t L - e -g t 1.0 P H t L - e -g t 1.0 0.01 0.02 t t 0.8 1 â 10 - 4 2 â 10 - 4 0.8 2 â 10 - 5 4 â 10 - 5 - 0.05 0.6 0.6 - 0.03 - 0.10 0.4 0.4 0.2 0.2 t t 1 â 10 - 5 2 â 10 - 5 3 â 10 - 5 4 â 10 - 5 5 â 10 - 5 0.5 â 10 - 4 1.0 â 10 - 4 1.5 â 10 - 4 2.0 â 10 - 4 2.5 â 10 - 4 (a) B − B res = 1 . 2 × 10 − 2 G (b) B − B res = 9 . 2 × 10 − 4 G notice how deviations from exp are enhanced for B close to resonance

finally: a surprise and open questions @ log H P H t LLD 2 2.0 1.5 1.0 0.5 t 1 â 10 - 4 2 â 10 - 4 3 â 10 - 4 4 â 10 - 4

finally: a surprise and open questions Im E pole @ log H P H t LLD 2 B = B 1 = B res + 2.64 â 10 - 5 G S III H E L B = B res Re E pole 2.0 S II H E L 1.5 1.0 0.5 t 1 â 10 - 4 2 â 10 - 4 3 â 10 - 4 4 â 10 - 4