Extreme decoherence and quantum chaos Adolfo d del C Campo DIPC & & Ike kerbasque Bilbao, S Spain QI QIST2019 Yuka kawa I Institute f for T Theoretical P Physics, 29 th th , 2 Kyoto U University, M May 2 2019 Adolfo d del C Campo
QST group from Boston to Bilbao Adolfo d del C Campo
QST group from Boston to Bilbao A Chenu AdC Dr. LP Garcia-Pintos Prof Zhenyu Xu F Gomez-Ruiz L Dupays Dr N Gentil TY Huang J Zhu Adolfo d del C Campo
Research Quantum open Systems Time, Quantum Speed Limits & Metrology Quantum Control: Shortcuts to Adiabaticity Dynamics of phase transitions: Kibble Zurek mechanism Quantum Computation: adiabatic, open Quantum Thermodynamics: engines, finite-time Trapped ions, cold atoms Integrable models, RMT, … Adolfo d del C Campo: ad adolfo.delcam ampo@umb.edu
Open Quantum Systems: Decoherence e.g. Zurek, Physics Today Adolfo d del C Campo
Contents u Extreme decoherence Noise as a resource for Open Quantum Systems Noise coupled to local interactions Noise coupled to Random Matrix Theory u Work statistics of complex systems Loschmidt echo and p(W) P(W) and scrambling Work pdf & chaos/RMT Work pdf for time-reversal Adolfo d del C Campo: ad adolfo.delcam ampo@umb.edu
Open Quantum Systems System of interest embedded in an environment: composite system-environment ρ ( t ) = ˆ U SE ( t, 0) ρ S (0) ⊗ ρ E ˆ U SE ( t, 0) † Reduced dynamics via master equation dt ρ S = − i d h i ˆ + D ( ρ S ) H S , ρ S ~ Markovian limit: Universal Lindblad form � dt ρ S = − i d α − 1 h i X ˆ L α ρ S L † L † � H S , ρ S α L α , ρ S + γ α ~ 2 α Adolfo d del C Campo
Open Quantum Systems: Decoherence Decay of coherences of density matrix, e.g. of a Schrodinger cat state � e − ( x − r )2 + e − ( x + r )2 ψ 0 ( x ) = N σ 2 σ 2 2 σ 2 e.g. Zurek, Physics Today Adolfo d del C Campo
Open Quantum Systems: Decoherence Decay of coherences of density matrix, e.g. of a Schrodinger cat state Quantum Brownian Motion dt ρ S ( t ) = 1 ~ [ x, { p, ρ S ( t ) } ] − 2 m γ k B T d i ~ [ H, ρ S ( t )] − i γ [ x, [ x, ρ S ( t )]] ~ 2 Decoherence time in the high-temperature limit λ 2 β τ D = 2 γ ∆ x 2 e.g. Zurek, Physics Today Adolfo d del C Campo
Decoherence from Quantum Decay: Fidelity Survival probability S ( t ) := F [ ρ S (0) , ρ S ( t )] = h Ψ 0 | ρ S ( t ) | Ψ 0 i Master equation � dt ρ S = − i d α − 1 h i X ˆ L α ρ S L † L † � H S , ρ S + α L α , ρ S γ α ~ 2 α Short time decay S ( t ) = 1 − t + O ( t 2 ) τ D Universal decoherence time for Markovian evolutions 1 τ D = Cov( A, B ) = h AB i � h A ih B i ⇣ ⌘ L α , L † P α γ α Cov α M. Beau, J. Kiukas, I. L. Egusquiza, AdC, Phys. Rev. Lett. 119, 130401 (2017) Adolfo d del C Campo
Decoherence from Quantum Decay: Purity Purity P t = tr ρ 2 S ∈ [1 /d, 1] Master equation � dt ρ S = − i d α − 1 h i X ˆ L α ρ S L † L † � H S , ρ S + α L α , ρ S γ α ~ 2 α Short time decay P t = P 0 [1 − Dt + O ( t 2 )] Universal decoherence time & rate 1 D = 2 1 τ D = ⇣ ⌘ L α , L † P α γ α Cov P 0 τ D α M. Beau, J. Kiukas, I. L. Egusquiza, AdC, Phys. Rev. Lett. 119, 130401 (2017) Adolfo d del C Campo
Decoherence from Quantum Decay Survival probability S ( t ) := F [ ρ S (0) , ρ S ( t )] = h Ψ 0 | ρ S ( t ) | Ψ 0 i Quantum Brownian motion dt ρ S ( t ) = 1 ~ [ x, { p, ρ S ( t ) } ] − 2 m γ k B T d i ~ [ H, ρ S ( t )] − i γ [ x, [ x, ρ S ( t )]] ~ 2 Short time decay S ( t ) = 1 − t + O ( t 2 ) τ D Recover Zurek’s estimate for decoherence time λ 2 β τ D = 2 γ ∆ x 2 M. Beau, J. Kiukas, I. L. Egusquiza, AdC, Phys. Rev. Lett. 119, 130401 (2017) Adolfo d del C Campo
Decoherence in Noisy Quantum systems Adolfo d del C Campo
Sources of noise Environment System Adolfo d del C Campo
Sources of noise Environment System I. L. Egusquiza et al ., Quantum evolution R. Gambini et al ., Fundamental according to real clocks, Phys. Rev. A 59 , decoherence from quantum gravity: 3236 (1999). a pedagogical review, J. Gen Relativ Gravit 39 , 1143 (2007). L. P. García-Pintos et al ., Wavefunction Collapse models A. Chenu et al ., Quantum Simulation of Spontaneous symmetry breaking (GRW theory, Milburn model, …) Generic Many-Body Open System induced by quantum monitoring, A. Bassi et al. Rev. Mod. Phys. 85 , 471 Dynamics Using Classical Noise, PRL 118 , arXiv:1808.08343. (2013) 140403 (2017). Adolfo d del C Campo
Stochastic Hamiltonians Full system Deterministic part + stochastic part with real Gaussian process H ( t ) = H 0 ( t ) + γ ( t ) V Stochastic Schrodinger equation i d dt | ψ ( t ) i = [ H 0 ( t ) + γ ( t ) V ] | ψ ( t ) i Extensive literature G. J. Milburn, PRA 44, 5401 (1991) H. Moya-Cessa, V. Bu ž ek, M. S. Kim, and P. L. Knight, PRA 48, 3900 (1993) A. Budini, PRA 64, 052110 (2001) […] A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Noise-Averaged dynamics Density matrix averaged over realizations ⌦ ↵ ρ ( t ) = h ρ st ( t ) i = | ψ ( t ) ih ψ ( t ) | Master equation requires stochastic unravelling Z t d h i V, h [ ˆ U st ( t, s ) V ˆ U † dt ρ ( t ) = � i [ H 0 ( t ) , ρ ] � ds h γ ( t ) γ ( s ) i st ( t, s ) , ρ st ( t )] i 0 Simplified via Novikov’s theorem for white noise h γ ( t ) γ ( t 0 ) i = W 2 δ ( t � t 0 ) dt ρ ( t ) = − i [ H 0 ( t ) , ρ ( t )] − W 2 d 2 [ V, [ V, ρ ( t )]] A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Experimental tests? Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain N X X ˆ J ij σ z i σ z σ x H I = − j − h i . i<j i =1 A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Experimental tests? Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain N X X ˆ J ij σ z i σ z σ x H I = − j − h i . i<j i =1 A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Experimental tests? Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain N X X ˆ J ij σ z i σ z σ x H I = − j − h i . i<j i =1 Modulating magnetic field X [ σ x i [ σ x D [ ρ ( t )] = − γ j , ρ ( t )]] ij Nonlocal “2-body” dissipator τ D ∼ 1 /N 2 A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Experimental tests? Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain N X X ˆ J ij σ z i σ z σ x H I = − j − h i . i<j i =1 A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Experimental tests? Quantum simulation of open systems with many-body dissipators Target Hamiltonian: Ising chain N X X ˆ J ij σ z i σ z σ x H I = − j − h i . i<j i =1 Modulating ferromagnetic couplings X X ⇥ σ z i σ z ⇥ σ z i 0 σ z ⇤⇤ D [ ρ ( t )] = − γ j 0 , ρ ( t ) j , i<j i 0 <j 0 Nonlocal “4-body” dissipator τ D ∼ 1 /N 4 A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Stochastic k-body Hamiltonians Stochastic Hamiltonian H S ( t ) = ˆ ˆ λ α ( t ) ˆ X H T ( t ) + L α α k-body operators L ( α ,k ) [ ˆ P, ˆ ˆ X L α ] = 0 , L α = i 1 ,...,i k i 1 < ··· <i k “2k-body” dissipators γ α 2 [ L ( α ,k ) i 1 ,...,i k , [ L ( α ,k ) X X X D ( ρ ) = − k , ρ ]] i 0 1 ,...,i 0 i 1 < ··· <i k i 0 1 < ··· <i 0 α k Double sum over indices vs usual single sum ~ correlated environment A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Stochastic k-body Hamiltonians Stochastic Hamiltonian H S ( t ) = ˆ ˆ λ α ( t ) ˆ X H T ( t ) + L α α k-body operators L ( α ,k ) [ ˆ P, ˆ ˆ X L α ] = 0 , L α = i 1 ,...,i k i 1 < ··· <i k “2k-body” dissipators τ D ∼ 1 /N 2 k Polynomial scaling A. Chenu, M. Beau, J. Cao, AdC, Phys. Rev. Lett. 118, 140403 (2017) Adolfo d del C Campo
Extreme Decoherence Adolfo d del C Campo
Chaos & Complex systems Chaotic systems as a paradigm of complex systems and test-bed for information scrambling Described by Random Matrix Theory Heavy Nucleus Systems Ensembles of random matrices Gaussian Unitary Ensembles (GUE): Hermitian Hamiltonians Gaussian Orthogonal Ensembles (GOE): Real Symmetric Hamiltonians with time-reversal symm Adolfo d del C Campo
Chaos & Complex systems Density of states: Universal for large Hilbert space dimension “d” ✓ E s √ ◆ 2 2 d ρ ( E ) = 1 − √ 2 d π N=100 (GUE) Eigenvalues spacing Adolfo d del C Campo
Stochastic k-body Hamiltonians Stochastic Hamiltonian H S ( t ) = ˆ ˆ λ α ( t ) ˆ X H T ( t ) + L α α RMT-body operators L ( α ,k ) [ ˆ P, ˆ ˆ X L α ] = 0 , L α = i 1 ,...,i k i 1 < ··· <i k Decoherence rate? Z. Xu, L. P. García-Pintos, A. Chenu, and AdC, PRL 122, 014103 (2019) Adolfo d del C Campo
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