We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning $δ$ and the nonlinear parameter $χ^{(3)}$ may be combined to yield a periodic dynamics and allowing the generation of almost exact superpositions of coherent states ({\sl Schrödinger} cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mixed field state (statistical mixture of two coherent states) evolves towards a pure field state ({\sl Schrödinger} cat) as well. We discuss the validity of those results by using the field fidelity and the {\sl Wigner} function.
Working from the Schroedinger's Cat paradigm, a series of experiments are constructed. The Bedford-Wang experiment is examined, and the ambiguity in its meaning is addressed. We eliminate this ambiguity by abandoning the idea of the triggering event, replacing the two-state system with a mirror that undergoes wave packet spreading. This creates an experimentally testable version of a modified Schroedinger's Cat experiment for which a null result is not the obvious outcome.
We give some arguments to evaluate the "size" of Schrodinger cat for the flux qubit, which has really different results from ref.[1] Korsbakken et al. [1] J.Korsbakken,F.K.Wilhelm and K.B.Whaley,Physics Scripta T137,014022 (2009)
Superpositions of macroscopically distinct quantum states, introduced in Schroedinger's famous Gedankenexperiment, are an epitome of quantum "strangeness" and a natural tool for determining the validity limits of quantum physics. The optical incarnation of Schroedinger's cat - the superposition of two opposite-amplitude coherent states - is also the backbone of quantum information processing in the continuous-variable domain. However, existing preparation methods limit the amplitudes of the component coherent states by about 2, which curtails the state's usefulness for fundamental and practica…
We propose a measure for the "size" of a Schroedinger cat state, i.e. a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties, by counting how many single-particle operations are needed to map one state onto the other. This definition gives sensible results for simple, analytically tractable cases and is consistent with a previous definition restricted to Greenberger-Horne-Zeilinger-like states. We apply our measure to the experimentally relevant, nontrivial example of a superconducting three-junction flux qubit put into a superposition of left- an…
In this paper we re-investigate the core of Schroedinger's 'cat paradox'. We argue that one has to distinguish clearly between superpositions of macroscopic cat states and superpositions of entangled states which comprise both the state of the cat. It is shown, that in the first instance recurrence to decoherence or other mechanisms is not necessary in this special case in order to explain the absence of macroscopic superpositions. Additionally, we present modified versions of two quantum optical experiments as experimenta crucis. Applied rigorously, quantum mechanical formalism reduces the pr…
Intriguing dichotomies in quantum measurement theory involving the role of the obersever, objective reality, collapse of wavefunctions and actualization of a measurement outcome are cast into a patholigical gedanken experiment involving a single electron in a double quantum dot system coupled via a weak link.
Contractive states for a free quantum particle were introduced by Yuen [Yuen H P 1983 Phys. Rev. Lett. 51, 719] in an attempt to evade the standard quantum limit for repeated position measurements. We show how appropriate families of two- and three component ``Schroedinger cat states'' are able to support non-trivial correlations between the position and momentum observables leading to contractive behavior. The existence of contractive Schroedinger cat states is suggestive of potential novel roles of non-classical states for precision measurement schemes.
An interferometric experiment is described that characterizes an optical cat state in a cavity mode. Our method describes how to measure the amplitude and phase of the different coherent states that make up the cat states. We show that using a recently proposed quantum nondemolition measurement technique, we can circumvent the problem of decoherence inherent in measurement involving superposition of coherent states.
This MSc dissertation surveys nine interpretations of non-relativistic quantum mechanics. Extensive references are given. The interpretations covered are: the orthodox interpretation, Bohr's interpretation, the idea that the mind causes collapse, hidden variables, the many-worlds interpretation, the many-minds interpretation, Bohm's interpretation and two interpretations based on decoherent histories.
The problem of photon adding and subtracting is studied, using conditional output measurement on a beam splitter. It is shown that for various classes of states the corresponding photon-added and -subtracted states can be prepared. Analytical results are presented, with special emphasis on photon-added and -subtracted squeezed vacuum states, which are found to represent two different types of Schroedinger-cat-like states. Effects of realistic photocounting and Fock-state preparation are discussed.
We propose a dynamical scheme for deterministically amplifying photonic Schroedinger cat states based on a set of optimal state-transfers. The scheme can be implemented in strongly coupled qubit-cavity systems and is well suited to the capabilities of state of the art superconducting circuits. The ideal analytical scheme is compared with a full simulation of the open Jaynes-Cummings model with realistic device parameters. This amplification tool can be utilized for practical quantum information processing in non-classical continuous-variable states.
We present a tomographic method for the reconstruction of the full entangled quantum state for the cyclotron and spin degrees of freedom of an electron in a Penning trap. Numerical simulations of the reconstruction of several significant quantum states show that the method turns out to be quite accurate.
After a careful analysis of the feedback model recently proposed by Slosser and Milburn [Phys. Rev. Lett. 75, 418 (1995)], we are led to the conclusion that---under realistic conditions---their scheme is not significantly more effective in the production of linear superpositions of macroscopically distinguishable quantum states than the usual quantum-optical Kerr effect.
The quantum state of Schroedinger's cat is usually incorrectly described as a superposition of "dead" and "alive," despite an argument by Rinner and Werner that, locally, the cat should be considered to be in a mixture of non-superposed states. Here, it is rigorously proven that the cat is not in a superposition. This is central to the measurement problem. Nonlocal two-photon interferometry experiments throw further light on the measurement state by probing the effect of a variable phase factor inserted between its superposed terms. These experiments demonstrate that both subsystems really are…
We review the use of quantum feedback for combatting the decoherence of Schroedinger-cat-like states in electromagnetic cavities, with special emphasys on our recent proposal of an automatic mechanism based on the injection of appropriately prepared ``probe'' and ``feedback'' Rydberg atoms. In the latter scheme, the information transmission from the probe to the feedback atom is directly mediated by a second auxiliary cavity. The detection efficiency for the probe atom is no longer a critical parameter, and the decoherence time of the linear superposition state can be significantly increased u…
The new process of quantum-injection into an optical parametric amplifier operating in entangled configuration is adopted to amplify into a large dimensionality spin 1/2 Hilbert space the quantum entanglement and superposition properties of the photon-couples generated by parametric down-conversion. The structure of the Wigner function and of the field's correlation functions shows a decoherence-free, multiphoton Schroedinger-cat behaviour of the emitted field which is largely detectable against the squeezed-vacuum noise. Furthermore, owing to its entanglement character, the system is found to…
We report preparation and characterization of coherent superposition states t |0> + alpha |1> of electromagnetic field by conditional measurements on a beamsplitter. The state is generated in one of the beam splitter output channels if a coherent state and a single-photon Fock state |1> are present in the two input ports and a single photon is registered in the other beam splitter output. The single photon thus plays a role of a "catalyst": it is explicitly present in both the input and the output channels of the interaction yet facilitates generation of a nonclassical state of light.
Recently, Frauchiger and Renner proposed a Gedankenexperiment, which was claimed to be able to prove that quantum theory cannot consistently describe the use of itself. Here we show that the conclusions of Frauchiger and Renner actually came from their incorrect description of some quantum states. With the correct description there will be no inconsistent results, no matter which quantum interpretation theory is used. Especially, the Copenhagen interpretation can satisfy all the three assumptions (C), (Q), and (S) of Frauchiger and Renner simultaneously, thus it has no problem consistently des…
A scheme for generating Schrödinger cat-like states of a single-mode optical field by means of conditional measurement is proposed. Feeding into a beam splitter a squeezed vacuum and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties that are very similar to those of superpositions of two coherent states with opposite phases. We present analytical and numerical results for the photon-number and quadrature-component distributions of the conditional states and their Wigner and Husimi functions. Further, we discuss…
A Macro-state consisting of N= 3.5 x 10^4 photons in a quantum superposition and entangled with a far apart single-photon state (Micro-state) is generated. Precisely, an entangled photon pair is created by a nonlinear optical process, then one photon of the pair is injected into an optical parametric amplifier (OPA) operating for any input polarization state, i.e. into a phase-covariant cloning machine. Such transformation establishes a connection between the single photon and the multi particle fields. We then demonstrate the non-separability of the bipartite system by adopting a local filter…
We consider a quantum superposition of Bose-Einstein condensates in two immiscible internal states. A decoherence rate for the resulting Schroedinger cat is calculated and shown to be a significant threat to this macroscopic quantum superposition of BEC's. An experimental scenario is outlined where the decoherence rate due to the thermal cloud is dramatically reduced thanks to trap engineering and "symmetrization" of the environment which allow for the Schroedinger cat to be an approximate pointer states.
We present a scheme of generating large-amplitude Schrödinger cat states and entanglement in a coupled system of nanomechanical resonator and single Cooper pair box (SCPB), without being limited by the magnitude of the coupling. It is shown that the entanglement between the resonator and the SCPB can be detected by a spectroscopic method.
We study the dynamics of classical and quantum systems linearly interacting with a classical environment represented by an infinite set of harmonic oscillators. The environment induces a dynamical localization of the quantum state into a generalized coherent state for which the $\hbar \to 0$ limit always exists and reproduces the classical motion. We describe the consequences of this localization on the behavior of a macroscopic system by considering the example of a Schroedinger cat.
We characterize the degree of entanglement of a subsystem of $k$ particles in a $N$-two level system ($k\leq N/2$) initially prepared in a mesoscopic superposition $|ψ>=\int dθf(θ) (|ϕ_{1}(θ)>^{\otimes N}+|ϕ_{2}(θ)>^{\otimes N})$, where $f(θ)$ is a gaussian or a delta function, subject to the time evolution described by a dephasing channel. Negativity is used as a measure of entanglement for such system. For an arbitrary number of particles $N$, numerical results are given for the full time evolution up to ten particles. Analytical results are obtained for short times and asymptotic time regim…
We study two-spin entanglement and order parameter fluctuations as a function of the system size in the XY model in a transverse field and in the isotropic XXX model. Both models are characterized by the occurrence of ground state degeneracy also when systems of finite size are considered. This is always true for the XXX model, but only at the factorizing field for the XY model. We study the size dependence of symmetric states, which, in the presence of degeneracy, can be expanded as a linear combination of broken symmetry states. We show that, while the XY model looses its quantum superpositi…
Heisenberg's principle$^1$ states that the product of uncertainties of position and momentum should be no less than Planck's constant $\hbar$. This is usually taken to imply that phase space structures associated with sub-Planck ($\ll \hbar$) scales do not exist, or, at the very least, that they do not matter. I show that this deeply ingrained prejudice is false: Non-local "Schrödinger cat" states of quantum systems confined to phase space volume characterized by `the classical action' $A \gg \hbar$ develop spotty structure on scales corresponding to sub-Planck $a = \hbar^2 / A \ll \hbar$. Suc…
Interferometry with NOON quantum states can provide unbiased phase estimation with a sensitivity scaling as $Δθ\sim 1/N_T$ given a prior knowledge that the true phase shift $θ$ lies in the interval $-π\leq θ\leq π$. The protocol requires a total of $N_T = 2^{p}-1$ particles (unequally) distributed among $p$ independent measurements and overcomes basic difficulties present in previously proposed approaches. We demonstrate the possibility to obtain a phase sensitivity beating the classical shot-noise limit using published probabilities retrieved experimentally for the creation of Schrödinger cat…
The transition from quantum to classical, in the case of a quantum harmonic oscillator, is typically identified with the transition from a quantum superposition of macroscopically distinguishable states, such as the Schrödinger cat state, into the corresponding statistical mixture. This transition is commonly characterized by the asymptotic loss of the interference term in the Wigner representation of the cat state. In this paper we show that the quantum to classical transition has different dynamical features depending on the measure for nonclassicality used. Measures based on an operatorial …
Highly quantum non-linear interactions between different bosonic modes lead to the generation of quantum non-Gaussian states, i.e. states that cannot be written as mixtures of Gaussian states. A paradigmatic example is given by Schroedinger's cat states, that is coherent superpositions of coherent states with opposite amplitude. We here consider a novel quantum non-Gaussianity criterion recently proposed in the literature and prove its effectiveness on Schroedinger cat states evolving in a lossy bosonic channel. We prove that quantum non-Gaussianity can be effectively detected for high values …
The Schroedinger equation with the nonlinear term is derived by the natural generalization of the hydrodynamical model of quantum mechanics. The nonlinear term appears to be logically necessary because it enables explanation of the classical limit of the wave function, the collaps of the wave function and solves the Schroedinger cat paradox.
We suggest a variant of the recently proposed experiment for the generation of a new kind of Schroedinger-cat states, using two coupled parametric down-converter nonlinear crystals [F. De Martini, Phys. Rev. Lett. 81, 2842 (1998)]. We study the parametric oscillator case and find that an entangled Schroedinger-cat type state of two cavities, whose mirrors are placed along the output beams of the nonlinear crystals, can be realized under suitable conditions.
I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical device associated with the observer plays an essential role. This leads me to postulate a ``principle of the integrity of the observer''. It essentially requires the observer to be part of a classical domain connected throughout the measurement process. Mathematically this naturally leads to a formulation of quantum mechanics as a kind of topological quantum field theory. Significantly, quantities wi…
The linearity of quantum mechanics leads, under the assumption that the wave function offers a complete description of reality, to grotesque situations famously known as Schroedinger's cat. Ways out are either adding elements of reality or replacing the linear evolution by a nonlinear one. Models of spontaneous wave function collapses took the latter path. The way such models are constructed leaves the question, whether such models are in some sense unique, i.e. whether the nonlinear equations replacing Schroedinger's equation, are uniquely determined as collapse equations. Various people work…
We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this theory, or introduce unusual and controversial interpretative rules and/or ontologies). To that effect, we recall a remarkable phenomenon in the…
In the first paper of this series, I introduced a non-linear, Hamiltonian, generalization of Schroedinger's theory that blocks formation of macroscopic dispersion ("cats"). But that theory was entirely deterministic, and so the origin of random outcomes in experiments such as Stern-Gerlach or EPRB was left open. Here I propose that Schroedinger's wavefunction has a random component and demonstrate that such an improvised stochastic theory can violate Bell's inequality. Repeated measurements and the back-reaction on the microsystem are discussed in a toy example. Experiments that might falsify …
We present a nonlinear stochastic Schroedinger equation for pure states describing non-Markovian diffusion of quantum trajectories. It provides an unravelling of the evolution of a quantum system coupled to a finite or infinite number of harmonic oscillators, without any approximation. Its power is illustrated by several examples, including measurement-like situations, dissipation, and quantum Brownian motion. In some examples, we treat the environment phenomenologically as an infinite reservoir with fluctuations of arbitrary correlation. In other examples the environment consists of a finite …
A non-Markovian stochastic Schroedinger equation for a quantum system coupled to an environment of harmonic oscillators is presented. Its solutions, when averaged over the noise, reproduce the standard reduced density operator without any approximation. We illustrate the power of this approach with several examples, including exponentially decaying bath correlations and extreme non-Markovian cases, where the `environment' consists of only a single oscillator. The latter case shows the decay and revival of a `Schroedinger cat' state. For strong coupling to a dissipative environment with memory,…
A simple model allows us to study the nonclassical behavior of slowly moving atoms interacting with a quantized field. Atom and field become entangled and their joint state can be identified as a mesoscopic "Schroedinger-cat". By introducing appropriate observables for atom and field and by analyzing correlations between them based on a Bell-type inequality we can show the corresponding nonclassical behavior.
The superposition principle is at the heart of quantum mechanics and at the root of many paradoxes arising when trying to extend its predictions to our everyday world. Schroedinger's cat is the prototype of such paradoxes and here, in contrast to many others, we choose to investigate it from the operational point of view. We experimentally demonstrate a universal strategy for producing an unambiguously distinguishable type of superposition, that of an arbitrary pure state and its orthogonal. It relies on only a limited amount of information about the input state to first generate its orthogona…
We consider a trapped ion with a quantized center-of-mass motion in 2D trap potential. With external laser fields the effective (non)linear coupling of two orthogonal vibrational modes can be established via stimulated Raman transition. Nonclassical vibrational states such as squeezed states or two-mode entangled states (Schroedinger cat-like states) can be generated. When the vibrational modes are entangled with internal energy levels the Greenberger-Horne-Zeilinger (GHZ) states can be prepared.
We study single photon optomechanics conditioned on photon counting events. By selecting only detection events that occur long after a photon pulse arrives at the cavity, the optomechanical interaction time can be increased, allowing a large momentum kick to be applied to the oscillator. We apply this to two optomechanical cavities set up within a Mach-Zhender interferometer driven by a single photon source. The conditional state of the mechanical modes in such a system becomes an entangled cat state for detection times resulting in maximum mechanical amplitude in phase space. Further we study…
We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schroedinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories revea…
We study the application of squeezed states in a quantum optical scheme for direct sampling of the phase space by photon counting. We prove that the detection setup with a squeezed coherent probe field is equivalent to the probing of the squeezed signal field with a coherent state. An example of the Schroedinger cat state measurement shows that the use of squeezed states allows one to detect clearly the interference between distinct phase space components despite losses through the unused output port of the setup.
We discuss the possibility of generating and detecting, by a tomographic reconstruction of the Wigner function, a macroscopic superposition of two coherent states. The superposition state is created using a conditioned measurement on the polarisation of a probe photon entangled to a coherent state. The entanglement is obtained using a Kerr cell inserted in a Mach-Zender interferometer. Some hint about generation of GHZ states is given as well.
We consider light scattering from ultracold atoms trapped in an optical lattice into a cavity. The measurement of photons leaking out the cavity provides a quantum nondemolition (QND) access to various atomic variables. Depending on the chosen geometry the time resolved light detection projects the atomic quantum state to various atom-number squeezed and Schroedinger cat states. Modifications of the atomic and light properties at a single quantum trajectory are demonstrated. The quantum structure of final states can be revealed by further observations of the same sample.
