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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Nonclassical effects in the photon-added thermal state

G Nelson Jones, Jeffrey Haight, Ching Tsung Lee

Published Jun 1, 1997• 62 citations
Publisher

Abstract

It was shown recently by Lee that, if a radiation state has zero probability of having zero photon, then the state is as nonclassical as possible. This suggests that one can convert any classical state into one of the most nonclassical states simply by adding one photon to it, which can be achieved by passing an excited atom through the cavity containing the classical radiation and accepting the resultant only if the exit atom is found to be in its ground state. This concept is applied to the thermal state as an illustration.

DOI
10.1088/1355-5111/9/3/011

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It was shown recently by Lee that, if a radiation state has zero probability of having zero photon, then the state is as nonclassical as possible. This suggests that one can convert any classical state into one of the most nonclassical states simply by adding one photon to it, which can be achieved by passing an excited atom through the cavity containing the classical radiation and accepting the resultant only if the exit atom is found to be in its ground state. This concept is applied to the thermal state as an illustration.
We show the experimental observation of quantum states of light exhibiting nonclassical features obtained by single photon excitation of a thermal state. Such single-photon-added thermal states are the result of the single action of the creation operator on a mixed state that can be fully described classically. They show different degree of nonclassicality depending on the mean photon number of the original thermal state. The generated state is characterized by means of ultra-fast homodyne detection which allows us to reconstruct its density matrix and Wigner function by quantum tomography. We demonstrate the nonclassical behavior of single-photon added thermal states by an analysis of the negativity of the Wigner function.
By the use of nonclassical depth as a criterion for nonclassicality, we show that states generated by first adding (subtracting) multiphotons to an arbitrary state and then subtracting (adding) multiphotons from the resulting state is certainly nonclassical if the addition number of photons is equal to or larger than the subtraction number. The explicit expressions of nonclassical depth are found for both the single-photon-subtracted Gaussian state and the photon-added-then-subtracted thermal state. Based on the expressions, we show that the nonclassicality of the initial Gaussian state can be enhanced by the photon subtraction process. We also notice that the photon-added-then-subtracted thermal state is nonclassical if the initial thermal mean photon number is not zero, and the nonclassicality increases monotonously as the initial thermal mean photon number increases.
Theoretical analysis is given of nonclassicality and decoherence of the field states generated by adding any number of photons to the squeezed thermal state (STS). Based on the fact that the squeezed number state can be considered as a single-variable Hermite polynomial excited state, the compact expression of the normalization factor is derived, a Legendre polynomial. The nonclassicality is investigated by exploring the sub-Poissonian and negative Wigner function (WF). The results show that the WF of single-photon–added STS (PASTS) always has negative values at the phase space center. The decoherence effect on PASTS is examined by the analytical expression of WF. It is found that a longer threshold value of decay time than in single-photon–subtraction STS is included in single PASTS.
Detecting nonclassical properties that do not allow classical interpretation of photoelectric counting events is one of the crucial themes in quantum optics. Observation of individual nonclassical effects for a single-mode field, however, has been so far practically confined to sub-Poissonian statistics and quadrature squeezing. We show that a photon-added classical (coherent or thermal) state exhibits generalized nonclassical features in all orders of creation and annihilation operators, thereby becoming a promising candidate for studying higher-order nonclassical effects. Our analysis demonstrates the robustness of these effects against nonideal experimental conditions.
In the recent years, effect of photon addition and subtraction to a quantum state of light is explored for coherent state, thermal state, Schrödinger cat state, Gaussian state and many more. It is reported that the phenomena of photon addition or subtraction significantly affect nonclassical properties of the states of light. Here we wish to study the effect of photon addition and subtraction to the binomial start of radiation on the nonclassical properties of the state. We observed that the depth of nonclassicality increases with photon addition and decreases with photon subtraction in antibunching and squeezing phenomenon. We also report significant changes in photon number distribution and variable with depending parameters.
Photon addition and subtraction are well-known to render Gaussian states non Gaussian. We evaluate how their optical nonclassicality is affected by the photon addition/subtraction process. It is known that photon addition always transforms a Gaussian state into a nonclassical state. We show that photon subtraction transforms classical states into classical ones and nonclassical ones into nonclassical ones. For a quantitative analysis of the resulting nonclassicality, we use a recently introduced nonclassicality witness, the quadrature coherence scale, and compute the relative nonclassicality gain of the single-photon added/subtracted Gaussian states with respect to the original Gaussian states. For arbitrary single-mode Gaussian states, we show that this relative gain can be substantial in both cases. Whereas the gain is always higher for photon-added states, it is only slightly so for a large parameter range and in particular in the limit of high squeezing, where both gains are identical. We also analyze the Wigner negative volume of the photon-added/subtracted states. Whereas photon-added Gaussian states are never Wigner positive, we show that single-mode photon-subtracted states are Wigner positive if and only if they are weakly nonclassical or classical. Our analysis relies on explicit and general expressions for the characteristic and Wigner functions of photon added/subtracted multi-mode Gaussian states that we obtain simply.