Abstract The magnitude enhancement of the Goos–Hänchen shift (GHS) in reflected light (RL) is investigated. We consider a cavity in which a four-level atomic medium with a double lambda ( )-type configuration is contained. By changing the relative phase of optical fields in the four-level atomic configuration, we obtain normal and anomalous dispersions. Similarly, the manipulation of the positive and negative GHS in the RL is explored via the control of the relative phase. In addition, we investigated the GHS in the RL with and without the Doppler broadening (DB) effect. Interestingly, giant GHS in the RL is revealed for the DB medium. The role of the Doppler width on the magnitude of the GHS in RL is also studied. We find that the magnitude of the negative and positive GHS in the RL increased via increasing the Doppler width.Abstract The magnitude enhancement of the Goos–Hänchen shift (GHS) in reflected light (RL) is investigated. We consider a cavity in which a four-level atomic medium with a double lambda ( )-type configuration is contained. By changing the relative phase of optical fields in the four-level atomic configuration, we obtain normal and anomalous dispersions. Similarly, the manipulation of the positive and negative GHS in the RL is explored via the control of the relative phase. In addition, we investigated the GHS in the RL with and without the Doppler broadening (DB) effect. Interestingly, giant GHS in the RL is revealed for the DB medium. The role of the Doppler width on the magnitude of the GHS in RL is also studied. We find that the magnitude of the negative and positive GHS in the RL increased via increasing the Doppler width.

Laser PhysicsMay 16, 20198 citations

A Kochen-Specker inequality

Ingemar Bengtsson, Luigi Accardi, Guillaume Adenier +5 more

AIP conference proceedingsJan 1, 20094 citations

Coherent Control of the Goos-Hänchen Shift in Polariton Optomechanics

Shah Fahad, Gao Xianlong

We propose a theoretical scheme for controlling the Goos-Hänchen shift (GHS) of a reflected probe field in a polariton optomechanical system. The system comprises an optical mode, a molecular vibrational mode, and $N$ excitonic modes, where excitons couple to molecular vibrations via conditional displacement interactions and to photons through electric dipole interactions. We show that the effective exciton-vibration coupling provides a powerful mechanism for coherent GHS control: in its absence, the system exhibits a pronounced GHS at resonance, while activating it strongly suppresses the shift. The effective cavity detuning and the cavity length serve as additional tunable parameters for GHS manipulation. Furthermore, increasing the collective exciton-optical coupling enhances the GHS. Our results establish a framework for probing the GHS in polariton optomechanical systems and offer new avenues for designing optical devices that exploit beam-displacement phenomena.We propose a theoretical scheme for controlling the Goos-Hänchen shift (GHS) of a reflected probe field in a polariton optomechanical system. The system comprises an optical mode, a molecular vibrational mode, and $N$ excitonic modes, where excitons couple to molecular vibrations via conditional displacement interactions and to photons through electric dipole interactions. We show that the effective exciton-vibration coupling provides a powerful mechanism for coherent GHS control: in its absence, the system exhibits a pronounced GHS at resonance, while activating it strongly suppresses the shift. The effective cavity detuning and the cavity length serve as additional tunable parameters for GHS manipulation. Furthermore, increasing the collective exciton-optical coupling enhances the GHS. Our results establish a framework for probing the GHS in polariton optomechanical systems and offer new avenues for designing optical devices that exploit beam-displacement phenomena.

physics.opticsCross-listedarXiv:2601.06876Jan 13, 2026

A Simple Note on the Leggett-Garg Inequality

Biswaranjan Panda

Jan 1, 20250 citations

Generalization of operator type Shannon inequality and its reverse one (Advanced Topics of Information Science and Functional Analysis)

Takayuki Furuta

We shall state the following generalization of operator type Shannoninequal- ity and its reverse one as a simple corollary of parametric extensions of Shannon inequality in Hilbert space operators.Let $\{A_{1}, A_{2}, \ldots, A_{n}\}$ andn $\{B_{1}, B_{2},\ldots, B_{n}\}n$ be two sequences of strictly positive operators on a Hilbert space H.If $E^{A_{j}=}L$ $B_{j}=I,$ thenwhere $S_{q}(A|B)=A^{\frac{1}{2}}(A^{\frac{-1}{2}}BA^{\frac{-1}{2}})^{q}(\log A^{\frac{-1}{2}}BA^{\frac{-1}{2}})A\mathrm{i}$ for $A>0$ , $B>0$ and any real number $q$ and $S(A|B)=S_{0}(A|B)=A^{\frac{1}{2}}(\log A^{\frac{-1}{2}}BA^{\frac{-1}{2}})A^{\frac{1}{2}}$ which is the relative operator entropy of $A>0$ and $B>0.$ Our results can be considered as parametric extensions of the following celebrated Shan- non inequality ( $[3],[5]$ and [233 $\mathrm{p},1]$ ) which is very useful and so famous in information theory.Let $\{a_{1}, a_{2}, \ldots, a_{n}\}$ and $\{b_{1}, b_{2}, \ldots, b_{n}\}$ be two probability vectors.Then $0 \geq\sum_{j=1}^{n}a_{j}\log b_{j}-\sum_{j=1}^{n}a_{j}\log a_{j}$ (see inequalities (2.4) of Corollary 2.4).We shall state the following generalization of operator type Shannoninequal- ity and its reverse one as a simple corollary of parametric extensions of Shannon inequality in Hilbert space operators.Let $\{A_{1}, A_{2}, \ldots, A_{n}\}$ andn $\{B_{1}, B_{2},\ldots, B_{n}\}n$ be two sequences of strictly positive operators on a Hilbert space H.If $E^{A_{j}=}L$ $B_{j}=I,$ thenwhere $S_{q}(A|B)=A^{\frac{1}{2}}(A^{\frac{-1}{2}}BA^{\frac{-1}{2}})^{q}(\log A^{\frac{-1}{2}}BA^{\frac{-1}{2}})A\mathrm{i}$ for $A>0$, $B>0$ and any real number $q$ and $S(A|B)=S_{0}(A|B)=A^{\frac{1}{2}}(\log A^{\frac{-1}{2}}BA^{\frac{-1}{2}})A^{\frac{1}{2}}$ which is the relative operator entropy of $A>0$ and $B>0.$Our results can be considered as parametric extensions of the following celebrated Shan- non inequality ( $[3],[5]$ and [233 $\mathrm{p},1]$ ) which is very useful and so famous in information theory.Let $\{a_{1}, a_{2}, \ldots, a_{n}\}$ and $\{b_{1}, b_{2}, \ldots, b_{n}\}$ be two probability vectors.Then $0 \geq\sum_{j=1}^{n}a_{j}\log b_{j}-\sum_{j=1}^{n}a_{j}\log a_{j}$ (see inequalities (2.4) of Corollary 2.4).

Oct 1, 20040 citations

Leggett-Garg inequalities

Eduard Bordas Marchante

Jan 1, 20180 citations

N

excitonic modes, where excitons couple to molecular vibrations via conditional displacement interactions and to photons through electric dipole interactions. We show that the effective exciton-vibration coupling provides a powerful mechanism for coherent GHS control: in its absence, the system exhibits a pronounced GHS at resonance, while activating it strongly suppresses the shift. The effective cavity detuning and the cavity length serve as additional tunable parameters for GHS manipulation. Furthermore, increasing the collective exciton-optical coupling enhances the GHS. Our results establish a framework for probing the GHS in polariton optomechanical systems and offer new avenues for designing optical devices that exploit beam-displacement phenomena.

\{A_{1}, A_{2}, \ldots, A_{n}\}

andn

\{B_{1}, B_{2},\ldots, B_{n}\}n

be two sequences of strictly positive operators on a Hilbert space H.If

E^{A_{j}=}L

B_{j}=I,

thenwhere

S_{q}(A|B)=A^{\frac{1}{2}}(A^{\frac{-1}{2}}BA^{\frac{-1}{2}})^{q}(\log A^{\frac{-1}{2}}BA^{\frac{-1}{2}})A\mathrm{i}

for

A>0

B>0

and any real number

q

and

S(A|B)=S_{0}(A|B)=A^{\frac{1}{2}}(\log A^{\frac{-1}{2}}BA^{\frac{-1}{2}})A^{\frac{1}{2}}

which is the relative operator entropy of

A>0

and

B>0.

Our results can be considered as parametric extensions of the following celebrated Shan- non inequality (

[3],[5]

and [233

\mathrm{p},1]

) which is very useful and so famous in information theory.Let

\{a_{1}, a_{2}, \ldots, a_{n}\}

and

\{b_{1}, b_{2}, \ldots, b_{n}\}

be two probability vectors.Then

0 \geq\sum_{j=1}^{n}a_{j}\log b_{j}-\sum_{j=1}^{n}a_{j}\log a_{j}

(see inequalities (2.4) of Corollary 2.4).