Selective linear or quadratic optomechanical coupling via measurement

The ability to engineer both linear and non-linear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical displacement coupling can be achieved using the optomechanical interaction linearly proportional to the mechanical position. The resulting square displacement measurement strength is compared to that attainable in the dispersive case using the direct interaction to the mechanical displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.Comment: 7 pages, 2 figures, (accepted in Physical Review X

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance

The "self-induced decoherence" (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and (2), that this process can be interpreted as decoherence. We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is likely to fail also in other systems composed of discrete subsystems. Regarding the second claim, we emphasize that SID does not describe a physically meaningful decoherence process for individual measurements, but only involves destructive interference that occurs collectively within an ensemble of presupposed "values" of measurements. This leads us to question the relevance of SID for treating observed decoherence effects.Comment: 11 pages, 4 figures. Final published versio

Delayed-choice quantum eraser for the undergraduate laboratory

In a delayed-choice quantum eraser, interference fringes are obtained by erasing which-way information after the interfering particle has already been irreversibly detected. Following an introductory review of delayed-choice experiments and quantum erasure, we describe the experimental realization of an optical delayed-choice quantum eraser, suitable for advanced undergraduates, based on polarization-entangled pairs of single photons. In our experiment, the delay of the erasure is implemented using two different setups. The first setup employs an arrangement of mirrors to increase the optical path length of the photons carrying which-way information. In the second setup, we use fiber-optic cables to elongate the path of these photons after their passage through the polarization analyzer but prior to their arrival at the detector. We compare our results to data obtained in the absence of a delay and find excellent agreement. This shows that the timing of the erasure is irrelevant, as also predicted by quantum mechanics. The experiment can serve as a valuable pedagogical tool for conveying the fundamentals of quantum mechanics.Comment: 13 pages, 5 figures, identical to published versio

Observation of the quantum paradox of separation of a single photon from one of its properties

We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called "quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer.Comment: 9 pages, 4 figures, identical to published versio

Energy transfer in finite-size exciton-phonon systems : confinement-enhanced quantum decoherence

Based on the operatorial formulation of the perturbation theory, the exciton-phonon problem is revisited for investigating exciton-mediated energy flow in a finite-size lattice. Within this method, the exciton-phonon entanglement is taken into account through a dual dressing mechanism so that exciton and phonons are treated on an equal footing. In a marked contrast with what happens in an infinite lattice, it is shown that the dynamics of the exciton density is governed by several time scales. The density evolves coherently in the short-time limit whereas a relaxation mechanism occurs over intermediated time scales. Consequently, in the long-time limit, the density converges toward a nearly uniform distributed equilibrium distribution. Such a behavior results from quantum decoherence that originates in the fact that the phonons evolve differently depending on the path followed by the exciton to tunnel along the lattice. Although the relaxation rate increases with the temperature and with the coupling, it decreases with the lattice size, suggesting that the decoherence is inherent to the confinement

On the origin of probability in quantum mechanics

I give a brief introduction to many worlds or "no wavefunction collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability.Comment: 7 pages, 2 figures. This version to appear as a Brief Review in Modern Physics Letter

Quantum Equilibration under Constraints and Transport Balance

For open quantum systems coupled to a thermal bath at inverse temperature $\beta$, it is well known that under the Born-, Markov-, and secular approximations the system density matrix will approach the thermal Gibbs state with the bath inverse temperature $\beta$. We generalize this to systems where there exists a conserved quantity (e.g., the total particle number), where for a bath characterized by inverse temperature $\beta$ and chemical potential $\mu$ we find equilibration of both temperature and chemical potential. For couplings to multiple baths held at different temperatures and different chemical potentials, we identify a class of systems that equilibrates according to a single hypothetical average but in general non-thermal bath, which may be exploited to generate desired non-thermal states. Under special circumstances the stationary state may be again be described by a unique Boltzmann factor. These results are illustrated by several examples.Comment: 8 pages, 1 figure, leaner presentation, to appear in PR

Towards violation of Born's rule: description of a simple experiment

Recently a new model with hidden variables of the wave type was elaborated, so called prequantum classical statistical field theory (PCSFT). Roughly speaking PCSFT is a classical signal theory applied to a special class of signals -- "quantum systems". PCSFT reproduces successfully all probabilistic predictions of QM, including correlations for entangled systems. This model peacefully coexists with all known no-go theorems, including Bell's theorem. In our approach QM is an approximate model. All probabilistic predictions of QM are only (quite good) approximations of "real physical averages". The latter are averages with respect to fluctuations of prequantum fields. In particular, Born's rule is only an approximate rule. More precise experiments should demonstrate its violation. We present a simple experiment which has to produce statistical data violating Born's rule. Since the PCSFT-presentation of this experiment may be difficult for experimenters, we reformulate consequences of PCSFT in terms of the conventional wave function. In general, deviation from Born's rule is rather small. We found an experiment amplifying this deviation. We start with a toy example in section 2. Then we present a more realistic example based on Gaussian states with very small dispersion, see section 3.Comment: The paper was completed with the description of an experiment with Gaussian states with very small dispersion. This experiment should induce violation of Born's rule, the fundamental law of Q