Vladimir Buzek

Optimal quantum clocks

Recent technical advances in the laser cooling and trapping of ions suggest that coherent manipulations of trapped ions will be performed in the not too far future [1]. Apart from various important applications such as quantum information processing or improving high-precision spectroscopy these techniques also allow us to test fundamental concepts of quantum theory. In particular, much deeper insight into the problem of quantum measurement can be obtained. In this Letter we study the problem of building an optimal quantum clock from an ensemble of N ions. To be specific let us assume an ion trap with N two-level ions all in the ground state jCl › j0l › ··· ›j 0 l. This state is an eigenstate of the free Hamiltonian and thus cannot record time. Therefore the first step in building a clock is to bring the system to an initial state ˆ V which is not an energy eigenstate. For instance one can apply a Ramsey pulse whose shape and duration is chosen such that it puts all the ions in the product state ˆ Vprod › ˆ r › ··· › ˆ r ;

Universal-NOT gate

Abstract The action of a NOT gate on a classical bit results in a change of its value from a 0 to a 1 and vice versa. The action of the classical NOT gate is in principle perfect because with fidelity equal to unity it complements the value of a bit. The action of the quantum NOT gate in a computational basis |0⟩ and |1⟩ is very similar to the action of the classical NOT gate. However, a more general quantum mechanical operation which corresponds to a classical NOT gate would take a qubit in an arbitrary state |Ψ⟩ and produce a qubit in the state |Ψ⊥⟩ orthogonal to |Ψ⟩. This operation is anti-unitary and therefore, cannot be realized exactly. So how well we can do? We find a unitary transformation acting on an input qubit and some auxiliary qubits, which represent degrees of freedom of the quantum NOT gate itself, which approximately realizes the NOT operation on the state of the original qubit. We call this ‘device’ a universal-NOT gate because the size of the error it produces is independent of the input state. We show that an optimal U-NOT gate which has as its input N identical qubits and produces M outputs achieves a fidelity of F = (N + 1)/ (N + 2), which is equal to the fidelity of estimation of the input qubits. We also show that when a priori information about the state of the input qubit is available, the fidelity of a quantum NOT gate can be much better than the fidelity of estimation.

Quantum simulations of optical systems

We show how two level atoms can be used to build microscopic models for mirrors and beamsplitters. The mirrors can have arbitrary shape allowing closed cavities to be built. It is possible to build networks or mirrors and beamsplitters and follow the time-evolution of the intensity of the radiation through the system.Abstract Within the framework of a two-dimensional microscopic, purely quantum mechanical model, we analyse the dynamics of single-photon wave packets interacting with optical elements (beam splitters, mirrors), modelled as systems of two-level atoms. That is, we utilize a two-dimensional cavity to simulate the quantum behaviour of simple optical components and networks made thereof. The field is quantized using the canonical procedure, and only the basis states with one unit of excitation are included. This, however, covers linear optical phenomena. The field is taken to interact with localized atoms through a dipole interaction. Using different configurations of atoms, and choosing their frequencies to be resonant or off-resonance, we can model mirrors, beam splitters, focusing devices and multicomponent systems. Thus we can model arbitrary linear networks of optical components. We show the time evolution of a photon wave packet in an interferometer as an example. As the state of the field is known at e...

Difference-phase squeezing from amplitude squeezing by means of a beamsplitter

A classical analysis of two equal intensity coherent fields incident on a beamsplitter shows that the difference-phase noise of the output depends only on the noise in the difference of the amplitudes of the input fields and not on their phase noise. This suggests that in the quantum mechanical case squeezing in the amplitudes of the input beams can lead to squeezing in the phase difference of the output beams. We show that this is true. We also find the phase properties of the output when the input consists of two number states with an equal number of photons. The difference phase distribution consists of two narrow peaks, at and . States with small phase difference noise should be useful in the measurement of phase shifts.

Decay of Quantum Coherences Under the Influence of a Thermal Heatbath

Recently several methods have been proposed for generation of superposition (Schrodinger cat) states in microwave cavities. At microwave frequencies thermal photons can significantly affect statistical properties of superposition states. In the present letter we study the influence of a thermal heatbath on non-classical properties of quantum superposition states. We show that at non-zero temperatures the loss of quantum coherences is much faster than at zero temperature and that the sensitivity of the quantum coherence to the presence of thermal photons can lead to some difficulties in the preparation of Schrodinger cat states in microwave cavities unless the temperature of the microwave cavity is sufficiently low.

Realization of POVMs using measurement-assisted programmable quantum processors

We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete POVMs. It is known that two unitary transformations implementable by the same programmable processor require mutually {\it orthogonal} states. It turns out that the situation with von Neumann measurements is different. Specifically, in order to realize two such measurements one does not have to use orthogonal program states. On the other hand, the number of the implementable von Neumann measurements is still limited. As an example of a programmable processor we use the so-called quantum information distributor.We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete positive-operator-valued measures. Nielsen and Chuang [Phys. Rev. Lett. 79, 321 (1997)] have shown that two unitary transformations implementable by the same programmable processor require mutually orthogonal states. We show that two different von Neumann measurements can be encoded into nonorthogonal program states. Nevertheless, given the dimension of a Hilbert space of the program register the number of implementable von Neumann measurements is still limited. As an example of a programmable processor we use the so-called quantum-information distributor.

Fluorescence from N three-level atoms in an ideal cavity

The problem of N three-level atoms interacting with two resonant cavity modes in an ideal cavity is considered. The spectral properties of the fluorescence field are discussed. It is shown that the sidebands of the fluorescence prove to be sources of the intense field ( approximately N2) which has sub-Poissonian statistics. The squeezing of the spectrum components is also discussed.

Amplitude-squared squeezing in collective resonance fluorescence

Abstract The amplitude-squared squeezing, defined by Hillery [M. Hillery, Phys. Rev. A 36 (1987) 3796], in collective resonance fluorescence is considered. Contrary to the single-atom case the amplitude-squared squeezing occurs in the mixture of sidebands of the collective fluorescence field. The enhancement of the degree of amplitude-squared squeezing is shown when the number of atoms increases. The influence of the thermal field on the amplitude-squared squeezing is also discussed.

Squeezing by nondegenerate four-wave mixing in a system of three-level atoms: effects of the thermal field

We have studied the generation of squeezing by nondegenerate four-wave mixing in a system of three-level atoms. The conditions for obtaining a large degree of squeezing in experiments with Rydberg atoms are given.