Abstract We investigate nonclassical properties of the quantum state generated by operating a two-mode Hadamard operator on the vacuum state. It is found that the scale length parameter of this new state plays an important role in squeezing. The anti-bunching effect, entanglement, and nonlocality are also derived analytically.
The concept of photon antibunching as a manifestation of nonclassical character in single-mode radiation is extended to two-mode radiation. A simple criterion for the existence of nonclassical effects in two-mode radiation is established. It implies that the intermode photon bunching, rather than antibunching, can play a key role in rendering two-mode radiation nonclassical. The two-mode squeezed vacuum states are used as simple examples to illustrate the essential point of the criterion. The criterion is then used to study the nonclassical properties of two types of two-mode squeezed states. A state generated by applying the squeeze operator to the two-mode vacuum first, followed by the displacement operator, is called a two-mode coherent squeezed state. If the order of the two operators is reversed, a two-mode squeezed coherent state is obtained. It is found that the latter has a much stronger tendency to become a nonclassical state than the former, assuming that the parameters involved are all the same. A measure of nonclassical depth of radiation is adopted. It is found that, according to this measure, the effect of squeezing in making two-mode coherent squeezed states nonclassical is not monotonic. Such phenomena do not occur in squeezed coherent states.
We theoretically construct a two-parameter two-mode squeezing operator by combining the two-mode coupled harmonic oscillator Hamiltonian with beam splitter transformations. A novel two-mode squeezed vacuum state (NTMSVS) is generated via the application of this operator to the two-mode vacuum state. Numerical investigations demonstrate that the NTMSVS exhibits intermediate properties between the conventional two-mode squeezed vacuum state (TMSVS) and the product state of two independent single-mode squeezed vacua across multiple quantum metrics, including Wigner distribution characteristics, logarithmic negativity, EPR steering robustness and Bell inequality violation. Notably, the quadrature squeezing and sum squeezing amplitudes are significantly amplified under specific parametric regimes, offering enhanced nonclassicality compared to standard squeezed states.
Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.
Quantum entanglement and squeezing are kinds of important nonclassical phenomena of quantum systems. In this paper entangling and squeezing properties of entangled coherent states are studied analytically and numerically. The realtions between two nonclassical effects of squeezing and entanglement are investigated in detail. It is found that the degree of squeezing can be increased or decreased through changing the degree of entanglement. And it is shown that squeezing properties of single-mode squeezing is very different from that of two-mode squeezing.
The properties of correlated two-mode SU(1, 1) coherent states are studied. These states are a generalization of the two-mode squeezed vacuum states and are generated by applying the two-mode squeeze operator to a state in which there are initially q photons in one mode, |q, 0〉, the squeezed vacuum (q = 0) obviously being a special case. For these states the photon-number distribution and the nonclassical properties of photon antibunching, enhanced phase fluctuations, violations of the Cauchy–Schwarz inequality, two-mode squeezing, and sum squeezing are studied. A Q-function quasi-probability distribution for these states is also presented.