Lecture 2: Quantum measurement, Schrödinger cat and decoherence

Transcription

1 Lecture 2: Quantum measurement, Schrödinger cat and decoherence 5

2 1. The Schrödinger cat 6

3 Quantum description of a meter: the "Schrödinger cat" problem One encloses in a box a cat whose fate is linked to the evolution of a quantum system: one radioactive atom. 7

4 The "Schrödinger cat" One closes the box and wait until the atom is desintegrated with a probability 1/2? When opening the box is the cat dead, alive or in a superposition of both? 8

5 "Schrödinger cat" and entanglement a vif + b mort Before opening the box, unitary evolution prepares a maximally atom-meter entangled state Does this state exists? That is a fundamental question for the quantum theory of measurement: how does the unphysical entanglement of SC state vanishes at the macroscopic scale. That is the problem of the transition between quantum and classical world 1 1 ( ) ( ) on a + b a, + b, Une mesure donne un résultat unique et pas une superposition. Comment les superpositions d'états étranges s'effacent-elle lors d'une mesure? processus de décohérence 9 on off on off on

6 Schrödinger cat and quantum measurement 1 1 ( ) ( ) on e + g e, + g, Real measurement provide one definite result and not superposition of results: SC states are unphysical Unitary evolution should not apply any more at "some scale". It seems that the atom-meter space contains to many states for describing reality Including dissipation due to the coupling of the meter to the environment will provide a physical mechanism "selecting" the physically acceptable states. on off on off on Let's lock at this in a real experiment using a meter whose size can be varied continuously from microscopic to macroscopic world. 10

7 2. detecting atoms with a mesoscopic field 11

8 A mesoscopic "meter": a coherent field states Number state: N Quasi-classical state: Photon number distribution N 2 α 2 α α = e N ; α = α e N! N Phase space representation iφ P(N) P ( N ) N N N = e ; N = α N! 0,4 Poisson distribution 0,3 0,2 N=2 0,1 0, Photon number N 2 Im(α) N. Φ > 1 α Φ 1 Re(α) Φ=1/ α N = 1/ α 12

9 QND detection of atoms using non-resonant interaction with a coherent field S Im(α) e Re(α) 13

10 QND detection of atoms using non-resonant interaction with a coherent field S Im(α) e e φ Re(α) e α e α. e iφ 0 14

11 QND detection of atoms using non-resonant interaction with a coherent field S Im(α) e e g e α e α. e iφ i g α g α. e Φ 0 0 φ φ g Re(α) a single atom controls the phase of the field The field phase "points" on the atomic state 15

12 QND detection of atoms using non-resonant interaction with a coherent field S R S Im(α) e e g π/2 pulse R 1 e α e α. e iφ i g α g α. e Φ 0 0 φ φ g Re(α) a single atom controls the phase of the field ( ) ( iφ iφ e + g α e α. e + g α. e ) The field phase "points" on the atomic state 16

13 Atom-meter entanglement ( ) ( iφ iφ e + g α e α. e + g α. e ) ( ) ( ) on e + g e, + g, 2 2 on off on off on This is a "Schrödinger cat state" Let us now consider the residual coupling of the cavity to the environment 17

14 The role of the "environment": For long atom-cavity interaction time field damping couples the system to the outside world a complete description of the system must take into account the state of the field energy "leaking" in the environment. General method for describing the role of the environment: field dρ 1 field 1 field = a a, ρ aρ a dt 2T + + T cav + + cav master equation of the field density matrix Physical result: decoherence τ dec τ N cav 18

15 The origin of decoherence: entanglement with the environment Environment Decay of a coherent field: α ( 0) vacuum α ( t) β ( t) env α ( t) = α ( ) 0. t e τ env cav the cavity field remains coherent the leaking field has the same phase as α no entanglement during decay 19

16 The origin of decoherence: entanglement with the environment Environment Decay of a "cat" state: Ψ cat vacuum 1 2 ( α ( t) β ( t) α ( t) β ( t) ) env cavity-environment entanglement: the leaking field "broadcasts" phase information env trace over the environment env decoherence (=diagonal field reduced density matrix) as soon as: β ( t) β ( t) 0 + env 20

17 The decoherence time α Environment Φ D: "Distance" between the two fields components. T decoh 2T = = D T N.2sin cav cav 2 2 ( Φ) Infinitely short decoherence time for macroscopic fields The Schröedinger cat does not exist! 21

18 3. Observing decoherence experimentally 22

19 Probing the coherence of the cat state Position (cm) D π/2 π/2 D Atom # 1 φ π/2 π/2 φ 4 2 Atom # 2 0 φ Non resonant phase shift in C τ Time "cat" state coherence Interference term in two atom correlation 23

20 Probing the cat coherence with the "mouse" atom Im(α) Atom # 1 Atom # 2 φ φ Re(α) 24

21 Probing the cat coherence with the "mouse" atom Im(α) Atom # 1 Atom # 2 φ φ Re(α) Two phase components of the field merge to the initial phase Quantum interference term in two atom correlation 25

22 Decoherence signal η(τ) n=3.3 δ/2π δ/2π=70 and 170 khz Time delay between atoms τ=t/τ cav 26

23 Quantum measurement: the role of the environment 1 Physical origin of decoherence: leak of information into the environment. The experimentalist does not kill the cat when opening the box: the environment knows whether the cat is dead or alive well before one opens the box. The environment performs continuously unread repeated measurement of the cat state The colapse of the quantum state can be considered as a shortcut to describe this physical process Does it solves the measurement problem? No: if the problem consists in telling how or why nature chooses randomly one classical state. Other alternative: many world interpretation of QM. Yes, once one a priori accepts the statistical nature of quantum theory. 27

24 Quantum measurement: the role of the environment 2 Objective definition of classical states as states which do not get entangled with the environment Definition of "pointer basis" of a meter: the pointer state of the meter is a classical state once decoherence occurs, the physical state of a meter is described by a diagonal density matrix in the pointer basis: e, g, ρ dec Pe 0 = 0 Pg at this level, quantum description only involves classical probabilities and no macroscopic superposition states. The decoherence approach shows that quantum theory is consistent with classical logic at macroscopic scale: it only provides classical statistics at the macroscopic scale. 28

25 Quantum physics and statistical physics Statistical physics describes partially complex classical system. The art of statistical physics consists in identifying the relevant macroscopic thermodynamic variable of a system. Quantum physics is very similar: for a complex open system, decoherence tells you what are the relevant classical states of the system. They correspond to well defined classical physical variables. Quantum theory then appear as a statistical theory of special macroscopic events named measurements. 29

26 Gedanken experiments/ real experiments Schrödinger 1952 : «one never experiments with just one electron, one atom or one molecule. In thought experiments we sometimes assume that we do, this invariably entails ridiculous consequences» (British Journal of the Philosophy of Sciences, vol 3, 1952) 30

27 Present members: PhD: Julien Bernu Samuel Deléglise Christine Guerlin Clément Sayrin Post-doc: Igor Dotsenko The team CQED Team +SK +SG Permanents: Jean-Michel Raimond Michel Brune Serge Haroche Superconducting atom chip team Former members: Stefan Kuhr (Mainz) Sébastien Gleyzes (post-doc Westbrook) Ulrich Hoff (diploma, Copenhagen) CEA Saclay (DAPNIA): P. Bosland, B. Visentin, E. Jacques. 31