Quantum states Schrodinger cats

The remarkable conclusion is that the microscopic quantum state, specified by the wave function ip, can be described on a macroscopic level by the probability distribution Pj. A single pure state corresponds to a macroscopic ensemble. The interference terms that are typical for quantum mechanics no longer appear. Incidentally, this resolves the paradox of Schrodinger s cat and, in general, the quantum mechanical measurement problem. )... 

This work is intended as an attempt to present two essentially different constructions of harmonic oscillator states in a FD Hilbert space. We propose some new definitions of the states and find their explicit forms in the Fock representation. For the convenience of the reader, we also bring together several known FD quantum-optical states, thus making our exposition more self-contained. We shall discuss FD coherent states, FD phase coherent states, FD displaced number states, FD Schrodinger cats, and FD squeezed vacuum. We shall show some intriguing properties of the states with the help of the discrete Wigner function. 

Here, we rq>ort related trapped-ion research at NIST on (1) the study of the dynamics of a two-level atomic system coupled to harmonic atomic motion, (2) the creation and characterization of nonclassical states of motion such as Schrodinger-cat superposition states, and (3) quantum logic for the generation of highly entangled states and for the investigation of scaling in a quantum computer. 

Analysis of this state is interesting from the point of view of the quantum measurement problem, an issue that has been debated since the inception of quantum theory by Einstein, Bohr, and others, and continues today [31]. One practical approach toward resolving this controversy is the introduction of quantum decoherence, or the environmentally induced reduction of quantum superpoations into clasacal statistical mbrtures [32], Decoherence provides a way to quantify the elusive boundary between classical and quantum worlds, and almost always precludes the existence of macroscopic Schrodinger-cat states, except for extremely short times. On the othm hand, the creation of mesoscopic Schrddinger-cat states like that of q. (10) may allow controlled studies of quantum decoherence and the quantum-classical boundary. This problem is directly relevant to quantum computation, as we discuss below. 

The state represented by Eq. (15) is of the same form as that ofEq. (10). Both involve entangled superpositions and both are subject to the destructive effects of decoherence. Creation of SchrOdinger cats like Eq. (10) is particularly relevant to the ion-based quantum computer because the primary source of decoherence will probably be due to decoherence of the n=0,l) motional states during the logic operations. 

Finally, Alex Brown et al. present in Chap. 9 some applications in the context of quantum computing. The possibilities offered through quantum computation have been well known for many years now [257,258]. A quantum computer is a computation device that makes direct use of quantum-mechanical phenomena, mainly the fact that the system can be in a coherent superposition of different eigenstates due to the superposition principle. This has no classical counterpart as illustrated by the famous Schrodinger cat as explained above. In classical computers, the basic unit of information is a bit that can have only two values often denoted 0 and 1. As explained by Brown et al, in quantum computers, the unit of information is a qubit that is a coherent superposition of two quantum sates denoted 0 and 1. More precisely, it is a two-state quantum-mechanical system that can be written as a 0 > >. The advantage of a quantum computer... 

Interactions between adjacent particles of condensed phases can lead to quantum correlations, quantum interference, entanglement and decoherence, delocalization and "Schrodinger s cat" states. Such effects are theoretically expected to be extremely short-lived, due to environmental disturbances. Therefore, it has been widely believed that they cannot be experimentally detected. However, based on previous theoretical work (cf. [Chatzidimitriou-Dreismann 1995 Chatzidimitriou-Dreismann 1997 (b)]), we proposed to detect QE in condensed systems by means of sufficiently "fast" scattering techniques. Particularly suitable for this purpose is the NCS method. Our NCS investigations (on liquid H2O - D2O mixtures [Chatzidimitriou-Dreismann 1997 (a)]) started 1995 and have provided, for the first time, direct experimental evidence of attosecond QE between a proton and its adjacent particles. 

One of the most famous thought experiments put forward in the early days of the quantum theory was formulated by Schrodinger and is now known as Schrodinger s cat This experiment called into question whether a system could have multiple acceptable wave functions prior to observation of the system. In other words, if we don t actually observe a system, can we know anything about the state it is in ... 

Schrodinger posed this paradox to point out weaknesses in some interpretations of quantum results, but the paradox has led instead to a continuing and lively debate about the fate and meaning of Schrodinger s cat. In 2012, the Nobel Prize in physics was awarded to Serge Haroche of France and David Wineland of the United States... 

Since the early days of quantum mechanics, many scholars were trying to rationalize the paradox, always relying on some particular interpretation of quantum mechanics. In one of the interpretations, quantum mechanics does not describe a single system, but rather an infinite set of systems. We have therefore plenty of cats and the same number of boxes, each of them with the same macabre gear inside. Then, the paradox disappears, because, after the boxes are open, in 50% of cases, the cats will be alive, and in 50%, they will be dead. In another interpretation, it is criticized that Schrddinger treats the box as a quantum system, while the observer is treated classically. In this interpretation, not only Schrodinger plays the role of the observer, but also the cat, and even the box itself (since it may contain a camera). What happened may be described differently by each of the observers, depending on what information they have about the whole system. For example, in the cat (alive or dead), there is information about what has happened even before the box is open. The human observer does not have this information. Therefore, the collapse of the wave function happened earlier for the cat and later for the observer Only after the box is open, it will turn out for both the cat and the observer that the collapse happened to the same state. 

Now here comes the absnrdity if the steel chamber is closed, the whole systan ranains unobserved, and the radioactive atom is in a state in which it has anitted the particle and not emitted the particle (with eqnal probabihty). Therefore, the cat is both dead and undead. Schrodinger put it this way [the steel chamba would have] in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts. When the chamber is opened, the act of observation forces the entire systan into one state or the other the cat is either dead or alive, not both. However, while unobserved, the cat is both dead and aUve. The absurdity of the both dead and undead cat in Schrodinger s thonght experiment was meant to demonstrate how quantum strangeness does not transfer to the macroscopic world. 

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