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Quantum probes versus direct measurements: What do we gain
- 1. Quantum probes versus direct measurements What do we gain? Sabrina Maniscalco S.Maniscalco@hw.ac.uk Institute of Photonics and Quantum Sciences Heriot-Watt University Edinburgh
- 2. Relativistic Quantum Metrology 7-8 March 2008, Nottingham
- 5. ?
- 6. M. Steiner et al., Phys. Rev. Lett. (2013) single trapped ion in optical fiber cavity
- 7. H. Ott’s group, Kaiserslauten Rb atoms in 2D optical lattice
- 9. initialize
- 10. initialize
- 11. engineer H
- 12. engineer H
- 13. read out
- 14. read out
- 16. Condensed Matter systems Superfluid Superfluid Mott insulator I. Bloch’s group, 2002
- 17. Condensed Matter systems Single-site addressing S. Kuhr’s and I. Bloch’s group
- 18. Open Quantum Systems trapped ions quantum simulator An open-system quantum simulator with trapped ions, Julio T. Barreiro, Markus Müller, Philipp Schindler, Daniel Nigg, Thomas Monz, Michael Chwalla, Markus Hennrich, Christian F. Roos, Peter Zoller and Rainer Blatt, Nature 470 , 486-491 (2011)
- 19. Dirac Equation trapped ions quantum simulator Quantum simulation of the Dirac equation R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt and C.F. Roos, Nature 463, 68 (2010)
- 20. 2D Ising Model trapped ions quantum simulator 100 N 350 Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins J.W. Britton, B.C. Sawyer, A.C. Keith, C.-C.J. Wang, J.K. Freericks, H. Uys, M.J. Biercuk, and J.J. Bollinger, Nature 484, 489 (2012)
- 25. Benchmarking
- 26. Benchmarking Problems with known solutions
- 27. Benchmarking Problems with known solutions Alternative measurement strategies
- 31. What if...
- 32. indirectly
- 33. indirectly
- 38. PROBE DECOHERENCE Depends on the state/properties of the complex systems m ex pl m Co te ys S
- 43. ⇢(t) = t ⇢(0) dynamical map quantum channel
- 45. t,0 = t,s s,0 Markovian dynamics Master equation in Lindblad form
- 46. Non-Markovian dynamics t,0 6= t,s s,0 Entanglement and Non-Markovianity of Quantum Evolutions Ángel Rivas, Susana F. Huelga, and Martin B. Plenio Phys. Rev. Lett. 105, 050403 (2010) On the degree of non-Markovianity of quantum evolution Dariusz Chruściński, Sabrina Maniscalco arXiv:1311.4213, in press in Phys. Rev. Lett.
- 47. Information flow
- 50. Quantum information and distinguishability between quantum states Increase of information Increase of distinguishability Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009) Measure for the non-Markovianity of quantum processes, Elsi-Mari Laine, Jyrki Piilo, and Heinz-Peter Breuer Phys. Rev. A 81, 062115 (2010)
- 51. Quantum information and distinguishability between quantum states Decrease of information Decrease of distinguishability
- 52. Distinguishability between two states of the Q probe 1 D(⇢1 , ⇢2 ) = Tr|⇢1 2 ⇢2 |, Rate of change of distinguishability d (t, ⇢1,2 (0)) = D(⇢1 (t), ⇢2 (t)) dt
- 53. Markovian dynamics (t, ⇢1,2 (0)) 0 at all times Non-Markovian dynamics (t, ⇢1,2 (0)) > 0 for some time intervals
- 54. MAXIMUM Information Backflow N ( ) = max ⇢1,2 (0) Z dt (t, ⇢1,2 (0)) >0 Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009) Measure for the non-Markovianity of quantum processes, Elsi-Mari Laine, Jyrki Piilo, and Heinz-Peter Breuer Phys. Rev. A 81, 062115 (2010)
- 55. MAXIMUM Information Backflow NC = NQ = Z Z C (t)dt C >0 Q (t)dt Q >0 Non-Markovianity and reservoir memory: A quantum information theory perspective B. Bylicka, D. Chruściński, S. Maniscalco, arXiv:1301.2585
- 59. Q PROBE strategy Quantifying information flow between the Q probe and the complex system / quantum simulator
- 60. Ability of a quantum probe to indirectly extract information on a complex quantum system
- 62. 2 Ising model in a transverse field
- 65. 2D 1D
- 67. Immersed probe atomic quantum dot Atomic Quantum Dots Coupled to a Reservoir of a Superfluid Bose-Einstein Condensate A. Recati, P. O. Fedichev, W. Zwerger, J. von Delft, and P. Zoller, Phys. Rev. Lett. 94, 040404 (2005) Probing BEC phase fluctuations with atomic quantum dots M. Bruderer, and D. Jaksch, New J. Phys. 8, 87 (2006)
- 68. Immersed probe atomic quantum dot Atomic Quantum Dots Coupled to a Reservoir of a Superfluid Bose-Einstein Condensate A. Recati, P. O. Fedichev, W. Zwerger, J. von Delft, and P. Zoller, Phys. Rev. Lett. 94, 040404 (2005) Probing BEC phase fluctuations with atomic quantum dots M. Bruderer, and D. Jaksch, New J. Phys. 8, 87 (2006)
- 69. 4 Impurity atom VA x 2L 2D BEC p VB x Figure 1. A Bose–Einstein condensate (yellow region) co harmonic trap VB (x) interacts with cold impurity atoms each Quantifying, characterizing and controlling information flow circle). The distance b in a double well Haikka, S. McEndoo,A (x) (grey in ultracoldS.atomic gases potential V G. De Chiara, M. Palma, and Maniscalco, P. Phys. Rev. A 84, 031602R (2011) the same trap is 2L and the distance between adjacent traps
- 70. 4 Impurity atom VA x 2L 2D BEC VB x Figure 1. A Bose–Einstein condensate (yellow region) confin harmonic trap VB (x) interacts with cold impurity atoms each of in a double well potential V A (x) (grey circle). The distance betw the same trap is 2L and the distance between adjacent traps is 2 QUANTUM PROBE HA = Z HB = describes the interactions between the impurities and the bath; here gAB = is the coupling constant of impurities–gas interaction, with aAB the scatteri impurities–gas collisions and m AB = m A m B /(m A + m B ) their reduced mass. B bath atoms are described in the second-quantized formalism. The field operat impurities ⇧ ˆ ⌥(x) = ai, p ⇧i, p (x) ˆ p2 A d3 x ˆ † (x) + VA (x) ˆ (x) 2mA QUANTUM GAS Z i, p can be decomposed in terms of the real eigenstates ⇧i, p (x) of impurity atoms double well i of the potential VA (x) in the p th state, with energy h ⌅i, p and th ¯ annihilation operator ai, p . We assume that the wavefunctions of different dou ˆ negligible common support, i.e. ⇧i, p (x)⇧ j⌅=i,m (x) ⇤ 0 at any position x. We treat the gas of bosons following Bogoliubov’s approach (see, for in assuming a very shallow trapping potential VB (x), such that the bosonic gas c homogeneous. In the degenerate regime, the bosonic field can be decomposed ⇧ ⌃ ⌃ ⇥ ˆ ˆ ⌃(x) = N0 ⌃0 (x) + ⌃(x) = N0 ⌃0 (x) + u k (x)ˆ k vk ( c p2 gB ˆ † 3 ˆ† B d x (x) + VB (x) + (x) ˆ (x) ˆ (x) 2mB 2 INTERACTION HAB = gAB Z k where ⌃0 (x) is the condensate wave function (or order parameter), N0 < N atoms in the condensate and ck , ck are the annihilation and creation operators o ˆ ˆ† ⇧ modes with momentum k. For a homogeneous condensate ⌃0 (x) = 1/ V , V b Its Bogoliubov modes ⌥ ⇤ ⌅ ik·x 1 ⇥k + n 0 gB e uk = +1 ⇧ , 2 Ek V d3 x ˆ (x) ˆ † (x) ˆ (x) ˆ (x) ⌥ ⇤ 1 ⇥k + n 0 gB vk = 2 Ek ⌅ ik·x e 1 ⇧ V
- 71. Qubit Probe |Li |Ri 4 Impurity atom VA x 2L 2D BEC p VB x Figure 1. A Bose–Einstein condensate (yellow region) co Pure DEPHASING harmonic trap VB (x) interacts with cold impurity atoms each in a double well potential V A (x) (grey circle). The distance b the same trap is 2L and the distance between adjacent traps
- 72. fo 4 a background gas particle. Furthermore, gk and ξk are te x coupling constants that depend on the spatial form Vof the p states |L and |R and on the shape of the Bogoliubov e modes. Their specific form is elaborated in Ref. [13]. is V When the background gas is at zero temperature the xreA condensate (yellow duced dynamics of the impurity atom harmonic trapBose–Einstein (x) (grey circle). Theatoms eachth is capturedwith cold impurity region) confin V (x) interacts by the of in a double well potential V distance betw N the same trap following time-local master equation (ME):is 2L and the distance between adjacent traps is 2 F describes the interactions between the impurities and the bath; here g = is the coupling constant of impurities–gas interaction, with a the scatteri if (t) dρ(t) impurities–gas 1 collisions and m = m m /(m + m ) their reduced mass. B ⇢ij (t) = e z , ρ] + γ(t)[σz ρ(t)σatoms are describedzinσzsecond-quantized formalism. The field operat ⇢ij (0) bath z − {σ the , ρ(t)}]. (2) M = Λ(t)[σ impurities dt 2 ⇧ aˆ ⇧ (x) p ˆ ⌥(x) = p Z t renormalizes the can be decomposed in termstherealqubit⇧ but atoms eigenstates (x) of impurity Quantity Λ(t) energy potentialofV the in the p state, with energy h¯ ⌅ andv double well i of the of (x) th annihilation operator a . We assume that the wavefunctions of different dou ˆ (t) qualitative (s) on the dissipativebosons ⇧following Bogoliubov’sany position(see, form ds effect negligible common support,dynamics. Ini.e. (x)⇧ (x) ⇤ 0 at x. has no = We treat the gas of approach in assuming very potential (x), such that 0 work we are interested a in shallow trappingregime, theVbosonic field canthe bosonic gasis stead in this the decay rate be decomposedc homogeneous. In the degenerate ⇧ ⌃ ⌃ ˆ ˆ ⌃(x) = N ⌃ (x) + ⌃(x) = N ⌃ (x) + u (x)ˆ a( c v 2 dk sin2 (k · L) where ⌃ (x) is thek t/¯ )wave function 2 τorder parameter), N < N sin(E condensate −k (or 2 /2 h 4gAB n0 atoms in the condensate and c , c aree annihilation and creation operators o ˆ ˆ the ,(x) = 1/⇧V , Vob γ(t) = (D) modes with momentum k. For a homogeneous condensate ⌃ h ¯ (2π)D n Its Bogoliubov modes + 2gB nD k ⌥ ⇤ ⌅ 1 ⇥ +n g e th u = +1 ⇧ , (3) 2 E V ⌥ ⇤ q ⌅ 1 ⇥ +n g e A Impurity atom 2L 2D BEC B Figure 1. B A AB AB AB A B A B i, p i, p i, p i, p th A i, p i, p i, p j⌅=i,m B 0 0 0 k 0 k k 0 0 † k k 0 k k vk = 0 B ik·x k k 2 0 B Ek ik·x 1 ⇧ V ⇥ k
- 73. Non-Markovianity: information flow Ndeph recoherence: 3D information backflow 2D 1D aB /aRb FIG. 2. (Color online) Non-Markovianity measure Ndeph as information lost in background gas aB a function of the scattering length of the the environment when the background gas is three dimensional (red dashed line), quasi-two dimensional (blue dotted line) and quasi-one decoherence: that the d reversed. Conclu in an ultr mersed in how preci fects the p s the manip tion flux. tally acce regimes, tion back for inform fundamen quantum for the re This w
- 74. Ndeph 3D 2D 1D aB /aRb FIG. 2. (Color online) Non-Markovianity measure Ndeph as a function of the scattering length of the background gas aB when the background gas is three dimensional (red dashed line), quasi-two dimensional (blue dotted line) and quasi-one dimensional (black solid line). The inset shows a longer range of the scattering length aB . In all figures the well separation Markovian to non-Markovian crossover that the d reversed. Conclu in an ultr mersed in how preci fects the s the manip p tion flux. tally acce regimes, tion back for inform fundamen quantum for the re This w dation, th MICINN
- 75. Ndeph 3D 2D 1D aB /aRb FIG. 2. (Color online) Non-Markovianity measure Ndeph as a function of the scattering length of the background gas aB when the background gas is three dimensional (red dashed line), quasi-two dimensional (blue dotted line) and quasi-one dimensional (black solid line). The inset shows a longer range of the scattering length aB . In all figures the well separation 3D 2D 1D that the d reversed. Conclu in an ultr mersed in how preci fects the s the manip p tion flux. tally acce regimes, tion back for inform fundamen quantum for the re This w dation, th MICINN
- 76. 2 Ising model in a transverse field em ex m Co pl t ys S
- 78. Hamiltonian of the spin chain H( ) = J X j z z j j+1 + x j
- 79. Hamiltonian of the spin chain H( ) = J X z z j j+1 + x j j Quantum phase transition /J ⌧ 1 /J = 1 /J 1 critical point (anti)ferromagnetic paramagnetic
- 80. Ising model trapped ions quantum simulator 16 spins quantum simulator H=J X i>j x x cij i j X y i i Emergence and Frustration of Magnetism with Variable-Range Interactions in a Quantum Simulator, R. Islam, C. Senko, W.C. Campbell, S. Korenblit, J. Smith, A. Lee, E.E. Edwards, J.C.C. Wang, J.K. Freericks, C. Monroe, Science, 340, 583 (2013)
- 81. paramagnetic phase | "y "y "y . . . i H=J X i>j /J = 5 x x cij i j X i y i
- 82. ferromagnetic phase | "x "x "x . . . i H=J X i>j cij x x i j X i /J = 0.01 | #x #x #x . . . i y i
- 83. 16 spins quantum simulator collective spin-dependent fluorescence measurements DESTRUCTIVE
- 84. 16 spins quantum simulator collective spin-dependent fluorescence measurements DESTRUCTIVE N=30 LIMIT TO CALCULATIONS OF DYNAMICS
- 85. can we measure the quantum phase transition indirectly, locally, and with minimal disturbance? ?
- 86. Q probe |eihe| |gihg| H( ) = J X z z j j+1 + x j j Hint ( ) = |eihe| X x j j H. T. Quan et al., Phys. Rev. Lett. 96, 140604 (2006)
- 87. @ Imperial http://youtu.be/RV1wykqg6rM Control of the conformations of ion Coulomb crystals in a Penning trap, S. Mavadia et al., Nature Communications 4, 2571 (2013)
- 88. PROBE Hint ( ) = |eihe| XSPINS x j j
- 89. Renormalised field ⇤ = ( + )/J
- 92. 1 qubit probe initialisation 1 (|ei + |gi) 2
- 93. 2 probe dynamics ⇢t = t ⇢0 DEPHASING
- 94. 1 2 change t 3 3 probe read out measure coherences N information flow
- 95. Number of spins Contour plot of N P. Haikka, J. Goold, S. McEndoo, F. Plastina, and S. Maniscalco, Phys. Rev. A 85, 060101(R) (2012)
- 96. N information flow dynamics of state distinguishability accessible information on the Q probe channel capacities DEPENDS ON THE SPIN CHAIN STATE
- 97. N =0 NO information backflow ONLY at critical point
- 99. N ions in a linear trap ⌫T transverse trap frequency ⌫C critical frequency
- 100. ⌫ T > ⌫C ⌫T = ⌫C ⌫ T < ⌫C critical point phase transition
- 101. 16 ions in a linear trap - Mainz experiment Observation of the Kibble–Zurek scaling law for defect formation in ion crystals S. Ulm et al Nature Communications 4, 2290 (2013)
- 102. Kibble–Zurek
- 104. Can we detect the structural phase transition by means of a local probe? ?
- 105. G. De Chiara, T. Calarco, S. Fishman, and G. Morigi, Phys. Rev. A 78, 043414 (2008)
- 106. G. De Chiara, T. Calarco, S. Fishman, and G. Morigi, Phys. Rev. A 78, 043414 (2008)
- 107. G. De Chiara, T. Calarco, S. Fishman, and G. Morigi, Phys. Rev. A 78, 043414 (2008)
- 109. 1 2 3 qubit probe initialisation probe dynamics Dephasing and dissipation probe read out Ramsey fringe interferometry
- 110. 1 2 change t 3 N information flow
- 111. 100 ions 1000 ions critical point M. Borrelli, P. Haikka, G. De Chiara, S. Maniscalco, Phys. Rev. A 88, 010101(R) (2013)
- 112. long range interaction Ion crystal 1000 short range interaction Ising model 800 600 N N 6= 0 400 200 structural phase transition quantum phase transition
- 113. Where we are now....
- 116. Quantum probes information flow between Q probe and complex system reveals properties of the latter one
- 117. properties of complex system (quantum simulator) are mapped into the decoherent dynamics of the Q probe
- 118. New tools Non-Markovianity measures Open Quantum System theoretical approaches
- 120. www.dscien.com
- 121. www.dscien.com
- 123. Funding:
- 124. Funding: