We study the reflection and transmission of a homonuclear diatomic molecule incident upon a potential barrier in one dimension. The effect of discrete and continuous unbound molecular states is investigated. We use the method of variable reflection and transmission amplitudes for discrete unbound states and we extend the method to include continuous unbound states. We take into account transitions between the bound and unbound states in the process of tunneling. For the molecule incident in a bound state, we calculate the probabilities of reflection and transmission in bound states as well as in unbound states. We focus on the molecule incident upon a $\ensuremath{\delta}$ barrier but we also investigate rectangular and Gaussian barriers. We show that transmission resonances are appreciably reduced by the inclusion of unbound states due to the lack of resonant structure in the probabilities of reflection and transmission in unbound states. We also find that much of the behavior of the molecule in the process of tunneling is primarily due to the bound states.We study the reflection and transmission of a homonuclear diatomic molecule incident upon a potential barrier in one dimension. The effect of discrete and continuous unbound molecular states is investigated. We use the method of variable reflection and transmission amplitudes for discrete unbound states and we extend the method to include continuous unbound states. We take into account transitions between the bound and unbound states in the process of tunneling. For the molecule incident in a bound state, we calculate the probabilities of reflection and transmission in bound states as well as in unbound states. We focus on the molecule incident upon a $\ensuremath{\delta}$ barrier but we also investigate rectangular and Gaussian barriers. We show that transmission resonances are appreciably reduced by the inclusion of unbound states due to the lack of resonant structure in the probabilities of reflection and transmission in unbound states. We also find that much of the behavior of the molecule in the process of tunneling is primarily due to the bound states.

Physical Review AMar 5, 200814 citations

SQUEEZING EFFECTS OF THE ATOMIC OPERATORS

WORLD SCIENTIFIC eBooksJul 1, 19980 citations

Central limits of squeezing operators

Luigi Accardi, Alexander Bach

Lecture notes in mathematicsJan 1, 198918 citations

Fundamental limits on determination of photon number statistics from measurements with multiplexed on/off detectors

Jaromír Fiurášek

We investigate fundamental bounds on the ability to determine photon number distribution and other related quantities from tomographically incomplete measurements with an array of M detectors that can only distinguish the absence or presence of photons. We show that the lower and upper bounds on photon number probabilities can be determined by solving a linear program. We present and discuss numerical results for various input states, including thermal states, coherent states, squeezed states, and highly nonclassical single-photon subtracted squeezed vacuum states. Besides photon number probabilities, we also investigate bounds on the parity of photon number distribution that determines the value of Wigner function of the state at the origin of phase space. Moreover, we also discuss estimation of mean photon number as an example of a quantity described by an unbounded operator. Our approach and results can provide quantitative guidance on the number of detection channels required to determine the photon number distribution with a given precision.We investigate fundamental bounds on the ability to determine photon number distribution and other related quantities from tomographically incomplete measurements with an array of M detectors that can only distinguish the absence or presence of photons. We show that the lower and upper bounds on photon number probabilities can be determined by solving a linear program. We present and discuss numerical results for various input states, including thermal states, coherent states, squeezed states, and highly nonclassical single-photon subtracted squeezed vacuum states. Besides photon number probabilities, we also investigate bounds on the parity of photon number distribution that determines the value of Wigner function of the state at the origin of phase space. Moreover, we also discuss estimation of mean photon number as an example of a quantity described by an unbounded operator. Our approach and results can provide quantitative guidance on the number of detection channels required to determine the photon number distribution with a given precision.

arXiv:2503.17480Physical Review ResearchJul 23, 20252 citations

Effect of squeezing operations in two-mode Gaussian quantum illumination

MuSeong Kim, Mi-Ra Hwang, Eylee Jung +1 more

Effect of the squeezing operations is examined in two-mode Gaussian quantum illumination. First, we consider two single-mode squeezing operation, whose squeezing parameters are $r_1$ and $r_2$ respectively. The final quantum Bhattacharyya (QB) bound between $\rho_0$ (state for target absence) and $\rho_1$ (state for target presence) is shown to be independent of $r_2$ . Compared to the classical coherent quantum illumination, we achieve the quantum advantage by $(6 + 10 \log_{10} (2 n_1 + 1))$ dB, where $n_1 = \sinh^2 r_1$ . Second, we examine the effect of the two-mode squeezing operation, whose squeezing parameter is $r$ . If $r \neq 0$ , the dominant term of the exponential factor in the resulting QB bound is independent of $N_S$ , where $N_S$ is the average photon number per signal mode. Since $N_S \ll 1$ is assumed, the tremendously huge quantum advantage can be achieved by controlling $r$ .Effect of the squeezing operations is examined in two-mode Gaussian quantum illumination. First, we consider two single-mode squeezing operation, whose squeezing parameters are $r_1$ and $r_2$ respectively. The final quantum Bhattacharyya (QB) bound between $\rho_0$ (state for target absence) and $\rho_1$ (state for target presence) is shown to be independent of $r_2$. Compared to the classical coherent quantum illumination, we achieve the quantum advantage by $(6 + 10 \log_{10} (2 n_1 + 1))$ dB, where $n_1 = \sinh^2 r_1$. Second, we examine the effect of the two-mode squeezing operation, whose squeezing parameter is $r$. If $r \neq 0$, the dominant term of the exponential factor in the resulting QB bound is independent of $N_S$, where $N_S$ is the average photon number per signal mode. Since $N_S \ll 1$ is assumed, the tremendously huge quantum advantage can be achieved by controlling $r$.

Nov 17, 20210 citations

The Floquet-Magnus expansion of unbounded operators

Daniel Burgarth, Robin Hillier, Davide Lonigro +1 more

The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly speaking, restricted to bounded Hamiltonians. In this work, we extend its definition and analysis to a broad class of time-periodic unbounded Hamiltonians. Our approach is based on an a priori distinct nonperturbative framework for the construction of effective Hamiltonians, which we show to reproduce the Floquet-Magnus expansion. A particular strength of our framework is that it allows us to prove that the resulting effective dynamics approximates the original time evolution propagators to arbitrary order in the high-frequency limit without requiring convergence of the Floquet-Magnus expansion, a condition that is already highly restrictive even in the bounded setting. We illustrate the scope of the method on representative models: the quantum Rabi Hamiltonian in the interaction picture, and the periodically driven quantum harmonic oscillator.The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly speaking, restricted to bounded Hamiltonians. In this work, we extend its definition and analysis to a broad class of time-periodic unbounded Hamiltonians. Our approach is based on an a priori distinct nonperturbative framework for the construction of effective Hamiltonians, which we show to reproduce the Floquet-Magnus expansion. A particular strength of our framework is that it allows us to prove that the resulting effective dynamics approximates the original time evolution propagators to arbitrary order in the high-frequency limit without requiring convergence of the Floquet-Magnus expansion, a condition that is already highly restrictive even in the bounded setting. We illustrate the scope of the method on representative models: the quantum Rabi Hamiltonian in the interaction picture, and the periodically driven quantum harmonic oscillator.

math-phCross-listedarXiv:2605.23734May 25, 2026

Effect of the squeezing operations is examined in two-mode Gaussian quantum illumination. First, we consider two single-mode squeezing operation, whose squeezing parameters are

r_1

and

r_2

respectively. The final quantum Bhattacharyya (QB) bound between

\rho_0

(state for target absence) and

\rho_1

(state for target presence) is shown to be independent of

r_2

. Compared to the classical coherent quantum illumination, we achieve the quantum advantage by

(6 + 10 \log_{10} (2 n_1 + 1))

dB, where

n_1 = \sinh^2 r_1

. Second, we examine the effect of the two-mode squeezing operation, whose squeezing parameter is

r

. If

r \neq 0

, the dominant term of the exponential factor in the resulting QB bound is independent of

N_S

, where

N_S

is the average photon number per signal mode. Since

N_S \ll 1

is assumed, the tremendously huge quantum advantage can be achieved by controlling

r