Muga G. Time in Quantum Mechanics - Vol. 2
Подождите немного. Документ загружается.
418 R. Wynands
172. E. Peik, B. Lipphardt, H. Schnatz, T. Schneider, Chr. Tamm, S.G. Karshenboim, Phys. Rev.
Lett. 93, 170801 (2004) 410, 411
173. S.N. Lea, Rep. Prog. Phys. 70, 1473 (2007) 410, 412
174. T.M. Fortier, N. Ashby, J.C. Bergquist, M.J. Delaney, S.A. Diddams, T.P. Heavner, L.
Hollberg, W.M. Itano, S.R. Jefferts, K. Kim, F. Levi, L. Lorini, W.H. Oskay, T.E. Parker,
J. Shirley, J.E. Stalnaker, Phys. Rev. Lett. 98, 070801 (2007) 410
175. S.G. Karshenboim, E. Peik, Eur. Phys. J. Special Topics 163, 1 (2008) 410
176. S. Bize, Y. Sortais, M.S. Santos, C. Mandache, A. Clairon, C. Salomon, Europhys. Lett. 45,
558 (1999) 410
177. E. Peik, B. Lipphardt, H. Schnatz, Chr. Tamm, S. Weyers, R. Wynands, arXiv:physics/
0611088v1 (2006) 411
Index
A
above-threshold ionization (ATI), 323
absorbing medium, 177
acousto-optic modulator, 190
Aharonov-Bohm effect, 313
Alice and Bob, 193
Allan
standard deviation, 370, 372
variance, 370, 372
Anandan-Aharonov relation, 350
anomalous dispersion, 176, 180
anti-bunching, 137
anti-Zeno effect, 205, 225, 231, 234, 235, 242,
264
antilinear operator, 343
arrow of time, 185, 242
astrology, 186
atom interferometry in the time domain, 304
atomic condensate, 278
atomic emission spectra, 291
attosecond double-slit, 320
avoided level crossing, 214
B
ballistic expansion, 212
band index, 214
band-gap edge, 278
blackbody shift, 391
Bloch equation, 145, 149, 152
Bloch oscillations, 218
Bloch sphere, 349, 351
Bloch theorem, 214
Bohr, Niels, 4
Born-Markov approximation, 284
Bose-Einstein condensate, 179
brachistochrone
classical, 341
quantum, 341
Brillouin precursor, 178
C
caesium atomic clock, 372
canonical commutation relation, 27
Cassirer, Ernst, 2
causality, 185, 187, 202
apparent violation, 199
center-of-mass motion, 161
centroid velocity, 178
clock, 185, 368
coherent population trapping, 400
energy, 6
history, 364
instability, 369
ion, 406
optical, 372, 402
pulsar, 408
synchronization, 186, 187
transition, 373, 384, 385, 389, 391, 398,
399, 403, 404, 406, 410–412
uncertainty, 369
coherence time, 313, 315, 316
coherent population oscillations (CPO), 179
coherent population trapping (CPT), 399
clock, 400
coherent states in Bargmann representation,
281
collapse of the wavefunction, 191
colored complex Gaussian noise, 283
complex conditional Hamiltonian, 132
two-level system, 132
complex potential, 66, 68, 69, 76, 78, 83, 87,
109, 264
complex time plane, 332
conditional time development, 129
confined time of arrival operator, 26, 44
conjugacy, 46
eigenfunction, 52
consistent histories, 259
Muga, J.G. et al.: Index. Lect. Notes Phys. 789, 419–423 (2009)
DOI 10.1007/978-3-642-03174-8
c
Springer-Verlag Berlin Heidelberg 2009
420 Index
continuous measurement, 281
and stochastic Schr
¨
odinger equations, 281
Coordinated Universal Time (UTC), 367
correspondence principle, 38
CPT adjoint, 344
current density, 69
measurement, 71
D
dark state, 399
decoherence, 277
delay time, 98
delay-bandwidth product, 180
delta-shell model, 253
Dick effect, 386, 387
diffraction in time, 303, 304, 316
diffraction of massive particles, 313
dipole force, 206
dipole matrix element, 210
Dirac equation for the neutrino, 15, 19
Dirac Hermitian adjoint, 343
dispersion relation, 296
double-slit
in space, 305
in time, 303, 309, 313
driving terms, 286
dwell time, 98
distribution, 100
free motion, 102
in a potential barrier, 106
operator, 99
operator, for n-particles, 114
second moment, 106
E
EAL, 366
Einstein coefficient, 135, 210
electromagnetically induced transparency
(EIT), 179
energy density, 177
energy velocity, 177
entanglement, 278
environment correlation function, 282
environment correlation time, 285
equivalence principle, 409
evanescent modes, 298
event, 25, 185, 187, 191
Event-Enhanced Quantum Theory (EEQT), 77
exponential decay, 239
exponential decay rate, 279
F
fast light, 176, 178–182, 187, 188, 190, 196,
202
Fermi Golden rule, 278
fine structure constant α, 411
first arrival, 54, 60
first photon, 71, 74–76, 88, 93
Fleming bound, 351, 354, 358, 359
fluorescence in a structured environment, 295
flux-flux correlation functions, ffcc, 99, 115,
117, 118, 120, 121, 123
fountain clock, 379
freeatomictimescale(EAL),366
front velocity, 177
Fubini-Study
line element, 349
metric, 349
G
Gamow states, 240
gauge invariance, 327, 337
gauge transformation, 326
Gaussian wave packet, 305–307
generalized Rabi frequency, 296
ghosts, 344
grating in time, 309
group velocity, 177–180, 194, 196
negative, 181, 183, 198
H
harmonic oscillator, 41
Heisenberg cut, 172
Heisenberg equations of motion, 280
hierarchy of equations for MTCF, 288
high-harmonic generation (HHG), 324
homodyne-heterodyne detection, 281
hydrogen maser, 401
I
information velocity, 177, 182, 201
initial state reconstruction, 259
International Atomic Time (TAI), 367
inverse square potentials, 255
ionization time, 329, 332, 333
K
Keldysh amplitude, 329
Keldysh parameter, 318
Kijowski’s time-of-arrival distribution, 69, 82,
84, 86, 88, 94
generalizations, 69
kinetic energy density, 87, 88
Kramers-Kronig relations, 180, 194
L
Landau-Zener tunneling, 226
laser–adapted interaction picture, 136
Index 421
length gauge, 327
level life-times, 130
light
cone, 175, 187
slow and fast, 191
light and dark periods, 128, 141
limited quantum decay, 278
Lindblad equation, 279
local densities, 69
local position invariance (LPI), 409
localization of light, 298
Lorentz oscillator, 177, 188
Lorentzian profile, 279
M
magneto-optical trap (MOT), 212, 314, 382
Majorana transition, 389
Maxwell’s equations, 15, 19, 20, 175, 176, 188
Maxwell–Lorentz-oscillator model, 189
measurement problem, 277
Mehlberg, Henry, 4
minimum coupling Hamiltonian, 326
Minkowski’s diagram, 187
Monte Carlo wave function approach, 280
Moshinsky’s shutter, 304
multiple-time correlation functions, 284, 285
N
Naimark dilation, 359
nanotechnology, 277
no-cloning theorem, 193
non-escape probability, 244
non-exponential decay, 227, 243, 279
non-Markovian master equation, 280
non-Markovian stochastic Schr
¨
odinger
equation, 281
normal dispersion, 180
O
operator normalization, 82, 84
operator ordering, 70
optical lattice, 206
optical model, 264
optical molasses, 212, 382
optical potential, 79
P
Paley-Wiener theorem, 245, 258
parity operator, 343, 356
passage time, 351, 353, 359
Pauli matrices, 353
Pauli’s theorem, 25, 66, 97, 98
phase velocity, 177
photon, 16
arriving, 192
description
classical, 16
quantum, 16
wave mechanical, 16
detection, 17, 74, 192
wave function, 18, 20, 22
photon-photon correlation, 21
photonic crystal, 180, 277, 278
pole expansion, 240
positive operator valued measure (POVM), 26,
66, 69, 359
positron, 10
post-exponential decay, 239–241, 243, 246,
247, 250, 252–254, 256–258, 260,
262–265, 268, 270, 271
in organic molecules, 242
power laws in organic molecules, 267
power spectrum, 293
Poynting vector, 177
precursor, 178, 189
projector formalism, 248
PT symmetry, 344
pulsar clock, 408
pulse front, 178, 189, 191, 201
pulse reshaping, 184
Q
quantization, 69
quantization rules, 65
quantum canonical pairs, 27
quantum computing, 277
quantum information, 359
quantum jump approach, 71, 81, 127, 280
quantum projection noise, 386
quantum regression theorem, 284
quantum state diffusion, 281
quantum theory of measurement, 61
quantum trajectory, 140, 149, 283, 330, 334
quantum tunneling, 225
quantum Zeno effect, 68, 89, 90, 130, 138,
172, 205, 231, 240, 264
optical analog, 271
quartic oscillator, 42
quasi-momentum, 214
R
Rabi frequency, 208, 376
Rabi pedestal, 377
radiation pressure, 206
radioactive dating, 242
Ramsauer resonance, 388
422 Index
Ramsey method, 375
recoil, 161
Redfield equation, 280
redshift
gravitational, 394
reduced propagators, 289
refractive index, 177, 178, 180, 194
Reichenbach, Hans, 2, 8–12
relativistic Doppler effect, 394
reset operation, 138
rigged Hilbert space, 35
Robertson-Schr
¨
odinger uncertainty principle,
91
rotating wave approximation, 132, 295
Rydberg constant Ry, 411
S
saddle-point time, 330, 331
saturation parameter, 210
scattering rate, 210
Schlick, Moritz, 1, 7
Schr
¨
odinger’s equation
time dependent, 15
Schr
¨
odinger-cat paradox, 313
Schulman’s relation, 93
second
definition, 364
redefinition, 407
second order approximation, 288
semiclassical equations of motion, 216
signal
definition of, 188
velocity, 177
simultaneity, 185
distant, 186
local, 185
slippage of initial conditions, 280
slow light, 178–180
Smith’s delay time, 108
Sommerfeld precursor, 178
speed of information transfer, 175
spin-flip, 352, 356, 357
spontaneous emission, 278
spontaneous force, 206
stimulated Brillouin scattering, 180
stimulated Raman scattering, 180
stochastic Schr
¨
odinger equation approach, 280
stochastic trajectory methods for MTCF, 289
strong-field approximation (SFA), 318, 328,
337
strong-field ionization, 317
structural resonances, 180
superluminal
communication, 188, 191, 193
propagation, 176, 184
stellar objects, 175
supraquantization, 34
survival probability, 244
T
TAI, 367
temporal non-locality, 58
time
as a parameter, 6, 22, 26, 66
definition of, 185
flow of, 185
time delay, 309
time dilation, 394
time direction, 10, 11
time observables, 65, 66, 97
time of arrival, 33, 65, 66, 68, 69, 71, 98, 164
distribution, 58, 76
operator, 33
time of flight, 65, 66, 304, 314, 316, 320, 321,
341, 346
time of residence, 112, 113
eigenvalues, 113
time operator, 304
time ordering, 138
time reflection, 343
time reversal, 250
time slits, 303, 309, 325, 331, 332, 334, 337
time-convolutionless master equations, 280
time-dependent interferometry, 313
time-energy
canonical commutation relation, 31, 61
uncertainty principle, 26
uncertainty relation, 3, 172, 304, 309, 313
time-reversal
invariance, 10
operator, 10, 343
symmetry, 39
times of transit, 197
Tonks-Girardeau gas, 253
tunneling, 317, 318, 324
two-level atom, 67, 132, 137, 156, 295
two-level tom, 93
two-time correlation functions, 284, 285
U
ultra-cold atoms, 179
unraveling of the master equation, 280
UTC, 367
Index 423
V
Van-Hove limit, 283
vector potential, 312, 319
Volkov-Hamiltonian, 327
von Neumann-L
¨
uders
projection postulate, 139
reduction rule, 130
W
w-function, 250
Wannier-Stark states, 218
Weisskopf-Wigner approximation, 240, 244,
247, 248
which-way information, 321