The generating function, the corresponding integrated intensity distribution, and the photon-counting distribution and its fractional moments are derived for the superposition of coherent and chaotic M-mode fields on the basis of a formalism of arbitrary ordering of field operators in quantum optics. An alternative description is also given based on a recent analysis of the superposition of coherent and chaotic fields in terms of the correlation functions which makes it possible to derive a number of results valid for arbitrary mean occupation numbers per mode from which the model considered follows as a special case. Many earlier results obtained for coherent and chaotic fields and their superposition are included as special cases. The present results generally describe a superposition experiment for an N-mode coherent field (e.g. generated by an N-mode laser operating far above threshold) and an M-mode chaotic field (M>or=N) as well as a field generated by an M-mode laser operating above threshold.The generating function, the corresponding integrated intensity distribution, and the photon-counting distribution and its fractional moments are derived for the superposition of coherent and chaotic M-mode fields on the basis of a formalism of arbitrary ordering of field operators in quantum optics. An alternative description is also given based on a recent analysis of the superposition of coherent and chaotic fields in terms of the correlation functions which makes it possible to derive a number of results valid for arbitrary mean occupation numbers per mode from which the model considered follows as a special case. Many earlier results obtained for coherent and chaotic fields and their superposition are included as special cases. The present results generally describe a superposition experiment for an N-mode coherent field (e.g. generated by an N-mode laser operating far above threshold) and an M-mode chaotic field (M>or=N) as well as a field generated by an M-mode laser operating above threshold.

Journal of physics. A, Proceedings of the Physical Society. GeneralNov 1, 196934 citations

Conditional quantum state engineering at beam splitter arrays

Clausen, J., Mohammed Dakna, L. Knoell +1 more

The generation of arbitrary single-mode quantum states from the vacuum by alternate coherent displacement and photon adding as well as the measurement of the overlap of a signal with an arbitrarily chosen quantum state are studied. With regard to implementations, the transformation of the quantum state of a traveling optical field at an array of beam splitters is considered, using conditional measurement. Allowing for arbitrary quantum states of both the input reference modes and the output reference modes on which the measurements are performed, the setup is described within the concept of two-port non-unitary transformation, and the overall non-unitary transformation operator is derived. It is shown to be a product of operators, where each operator is assigned to one of the beam splitters and can be expressed in terms of an s-ordered operator product, with s being determined by the beam splitter transmittance or reflectance. As an example we discuss the generation of and overlap measurement with Schroedinger-cat-like states.The generation of arbitrary single-mode quantum states from the vacuum by alternate coherent displacement and photon adding as well as the measurement of the overlap of a signal with an arbitrarily chosen quantum state are studied. With regard to implementations, the transformation of the quantum state of a traveling optical field at an array of beam splitters is considered, using conditional measurement. Allowing for arbitrary quantum states of both the input reference modes and the output reference modes on which the measurements are performed, the setup is described within the concept of two-port non-unitary transformation, and the overall non-unitary transformation operator is derived. It is shown to be a product of operators, where each operator is assigned to one of the beam splitters and can be expressed in terms of an s-ordered operator product, with s being determined by the beam splitter transmittance or reflectance. As an example we discuss the generation of and overlap measurement with Schroedinger-cat-like states.

arXiv:quant-ph/9905085May 25, 19993 citations

On the normal and antinormal ordering of field operators in quantum optics

Jan Peřina

Physics Letters AJun 1, 19673 citations

Configuration-Space Photon Number Operators in Quantum Optics

L. Mandeļ

Some properties of the operator ${\stackrel{^}{n}}_{V,t}$ representing the number of photons localized in a finite volume $V$ at time $t$ are investigated. To some extent these properties reflect the well-known difficulty of localizing photons in space-time. However, it is shown that, when the linear dimensions of $V$ are large compared with the wave-length of any occupied mode of the field, the ${\stackrel{^}{n}}_{V,t}$ operator acquires some simple properties. The commutator of ${\stackrel{^}{n}}_{V,t}$ and the detection operator $\stackrel{^}{\mathrm{A}}(\mathrm{x}, t)$ is expressible in an interesting form. The commutator and relations derived from it become particularly simple for certain space-time regions which we label conjoint and disjoint. An orthogonal set of eigenstates of ${\stackrel{^}{n}}_{V,t}$ is found, together with the corresponding eigenvalues, and it is shown that an arbitrary state is expressible in terms of these eigenstates. Some $N\mathrm{th}$ -order correlations of the ${\stackrel{^}{n}}_{V,t}$ operators are evaluated, and the results are used to calculate the probability distribution of eigenvalues of ${\stackrel{^}{n}}_{V,t}$ for an arbitrary state of the field.Some properties of the operator ${\stackrel{^}{n}}_{V,t}$ representing the number of photons localized in a finite volume $V$ at time $t$ are investigated. To some extent these properties reflect the well-known difficulty of localizing photons in space-time. However, it is shown that, when the linear dimensions of $V$ are large compared with the wave-length of any occupied mode of the field, the ${\stackrel{^}{n}}_{V,t}$ operator acquires some simple properties. The commutator of ${\stackrel{^}{n}}_{V,t}$ and the detection operator $\stackrel{^}{\mathrm{A}}(\mathrm{x}, t)$ is expressible in an interesting form. The commutator and relations derived from it become particularly simple for certain space-time regions which we label conjoint and disjoint. An orthogonal set of eigenstates of ${\stackrel{^}{n}}_{V,t}$ is found, together with the corresponding eigenvalues, and it is shown that an arbitrary state is expressible in terms of these eigenstates. Some $N\mathrm{th}$-order correlations of the ${\stackrel{^}{n}}_{V,t}$ operators are evaluated, and the results are used to calculate the probability distribution of eigenvalues of ${\stackrel{^}{n}}_{V,t}$ for an arbitrary state of the field.

Physical ReviewApr 29, 1966138 citations

Ordering of field operators and equations of motion in quantum optics

A. Lukš, Vlasta Peřinová

Czechoslovak Journal of PhysicsNov 1, 198712 citations

Some properties of the operator ${\stackrel{^}{n}}_{V,t}$ representing the number of photons localized in a finite volume

V

at time

t

are investigated. To some extent these properties reflect the well-known difficulty of localizing photons in space-time. However, it is shown that, when the linear dimensions of

V

are large compared with the wave-length of any occupied mode of the field, the ${\stackrel{^}{n}}_{V,t}$ operator acquires some simple properties. The commutator of ${\stackrel{^}{n}}_{V,t}$ and the detection operator $\stackrel{^}{\mathrm{A}}(\mathrm{x}, t)$ is expressible in an interesting form. The commutator and relations derived from it become particularly simple for certain space-time regions which we label conjoint and disjoint. An orthogonal set of eigenstates of ${\stackrel{^}{n}}_{V,t}$ is found, together with the corresponding eigenvalues, and it is shown that an arbitrary state is expressible in terms of these eigenstates. Some

N\mathrm{th}

-order correlations of the ${\stackrel{^}{n}}_{V,t}$ operators are evaluated, and the results are used to calculate the probability distribution of eigenvalues of ${\stackrel{^}{n}}_{V,t}$ for an arbitrary state of the field.