Squeezed light states have a special place in quantum optics with potentially profound applications in emerging quantum technologies. We present a numerically-exact matrix product states (MPS) approach to model quantum pulses of squeezed light, at the few-photon level, interacting with a two-level system in a waveguide environment. We represent the squeezed state as a coherent superposition of Fock states and explore the nonlinear population dynamics as well as multi-photon correlation functions that emerge. We show how the squeezed pulse can create quantum correlations that are unique to squeezed pulses, including $\langle b(t) b(t+t')\rangle$ for transmitted fields as well as $\langle b^\dagger(t) b^\dagger(t+t') b(t+t') b(t) \rangle$ . We also demonstrate how $\langle b(t) b(t+t') \rangle$ , a first-order correlation function, shows nonlinear photon correlations that are similar to those known and measured for two-photon scattering states. Finally, we also study the squeezed spectra of the pulse before and after interacting with the two-level system, and highlight the role of the spectral bandwidth of the incident pulse. The MPS theory allows the modeling of arbitrary bandwidth squeezing without making any Markov and Born approximations for the light-matter interaction processes, and can easily be extended to waveguide systems with multiple emitters and time-delayed feedback.Squeezed light states have a special place in quantum optics with potentially profound applications in emerging quantum technologies. We present a numerically-exact matrix product states (MPS) approach to model quantum pulses of squeezed light, at the few-photon level, interacting with a two-level system in a waveguide environment. We represent the squeezed state as a coherent superposition of Fock states and explore the nonlinear population dynamics as well as multi-photon correlation functions that emerge. We show how the squeezed pulse can create quantum correlations that are unique to squeezed pulses, including $\langle b(t) b(t+t')\rangle$ for transmitted fields as well as $\langle b^\dagger(t) b^\dagger(t+t') b(t+t') b(t) \rangle$. We also demonstrate how $\langle b(t) b(t+t') \rangle$, a first-order correlation function, shows nonlinear photon correlations that are similar to those known and measured for two-photon scattering states. Finally, we also study the squeezed spectra of the pulse before and after interacting with the two-level system, and highlight the role of the spectral bandwidth of the incident pulse. The MPS theory allows the modeling of arbitrary bandwidth squeezing without making any Markov and Born approximations for the light-matter interaction processes, and can easily be extended to waveguide systems with multiple emitters and time-delayed feedback.

quant-pharXiv:2608.06590Aug 10, 20260 citations

Experimental realization of spatially separated entanglement with continuous variables using laser pulse trains

Yun Zhang, Ryuhi Okubo, Mayumi Hirano +2 more

Spatially separated entanglement is demonstrated by interfering two high-repetition squeezed pulse trains. The entanglement correlation of the quadrature amplitudes between individual pulses is interrogated. It is characterized in terms of the sufficient inseparability criterion with an optimum result of in the frequency domain and in the time domain. The quantum correlation is also observed when the two measurement stations are separated by a physical distance of 4.5 m, which is sufficiently large to demonstrate the space-like separation, after accounting for the measurement time.Spatially separated entanglement is demonstrated by interfering two high-repetition squeezed pulse trains. The entanglement correlation of the quadrature amplitudes between individual pulses is interrogated. It is characterized in terms of the sufficient inseparability criterion with an optimum result of in the frequency domain and in the time domain. The quantum correlation is also observed when the two measurement stations are separated by a physical distance of 4.5 m, which is sufficiently large to demonstrate the space-like separation, after accounting for the measurement time.

Scientific ReportsAug 17, 201513 citations

Photon Correlation of Correlated Photons

John Rarity, P. R. Tapster

Springer eBooksJan 1, 19970 citations

Photon correlations in the homodyne detection of squeezed light

Daniel B. Erenso, Hua Deng, Reeta Vyas +1 more

Springer eBooksJan 1, 20031 citation

Photon number squeezing with a noisy fiber amplifier source by balanced detection technique

Shota Sawai, Hikaru Kawauchi, Kenichi Hirosawa +1 more

Summary form only given. Squeezed light at telecommunication wavelength is important source in the field of quantum information and communication technology, especially for realization of entanglement state with continuous variables. However, erbium-doped fiber amplifier (EDFA) used in classical communication systems contains substantially high intensity noise which is much higher than the shot noise level (SNL) due to beat noise of amplified spontaneous emission. Therefore, alternatively, optical parametric oscillators and Cr:YAG lasers have been employed for generation of squeezed light. In this work, we achieved photon number squeezing at 1.55 μm using a noisy EDFA laser as a light source, making use of collinear balanced detection technique, demonstrated by Nose et al.[1]. This technique compensates intensity noise at a specific radio-frequency by means of pulse splitting and recombination with a relative time delay τ. The photocurrent contributed by pulse trains is given by I(t) = I1(t) + I2(t) = I1(t) + I1(t-τ), where I1(t) and I2(t) is the photocurrent contributed by the first and second pules, respectively. The equation does not contain an interference term because any pulse does not temporally overlap each other. In the Fourier domain,we can obtain I(ω) = I1(ω) + I2(ω) = I1(ω) + I1(ω)exp(iωτ) and confirm the photocurrents are added up destructively at ω = π/τ. In our experiment, laser pulses, of which intensity noise is higher than 10dB from SNL, were divided into two parts and each of them experienced self-phase modulation during propagation through two different single-mode optical fibers. We detected the two pulse trains with a relative time delay and observed photon number squeezing a specific frequency. We used a femtosecond fiber laser (Femtolite, IMRA) as a light source. The center wavelength was 1560 nm and the repetition rate was 47.5 MHz. Figure 1 shows the experimental setup. We added time delay τ=1/frep, where frep is the repetition frequency, to one of the two pulse trains and added another delay deltaτ for preventing optical interference. We confirmed that intensity noise of the two pulse trains colineared at a polarization beam splitter (PBS) was coincident to the SNL both before and after fiber propagation at 22MHz. SNL was measured by balanced homodyne detection. We employed nonlinear polarization interferometer to generate squeezed light[2]. For measuring photon number squeezing, a branch ratio at PBS1 and PBS3,4 was adjusted to 90:10 and 95:5, respectively. We constructed another Michelson interferometer after a beam splitter to compensate the difference of fiber length. As a result, a maximum photon-number squeezing of 2.6 dB was obtained when average power was 4mW.Summary form only given. Squeezed light at telecommunication wavelength is important source in the field of quantum information and communication technology, especially for realization of entanglement state with continuous variables. However, erbium-doped fiber amplifier (EDFA) used in classical communication systems contains substantially high intensity noise which is much higher than the shot noise level (SNL) due to beat noise of amplified spontaneous emission. Therefore, alternatively, optical parametric oscillators and Cr:YAG lasers have been employed for generation of squeezed light. In this work, we achieved photon number squeezing at 1.55 μm using a noisy EDFA laser as a light source, making use of collinear balanced detection technique, demonstrated by Nose et al.[1]. This technique compensates intensity noise at a specific radio-frequency by means of pulse splitting and recombination with a relative time delay τ. The photocurrent contributed by pulse trains is given by I(t) = I1(t) + I2(t) = I1(t) + I1(t-τ), where I1(t) and I2(t) is the photocurrent contributed by the first and second pules, respectively. The equation does not contain an interference term because any pulse does not temporally overlap each other. In the Fourier domain,we can obtain I(ω) = I1(ω) + I2(ω) = I1(ω) + I1(ω)exp(iωτ) and confirm the photocurrents are added up destructively at ω = π/τ. In our experiment, laser pulses, of which intensity noise is higher than 10dB from SNL, were divided into two parts and each of them experienced self-phase modulation during propagation through two different single-mode optical fibers. We detected the two pulse trains with a relative time delay and observed photon number squeezing a specific frequency. We used a femtosecond fiber laser (Femtolite, IMRA) as a light source. The center wavelength was 1560 nm and the repetition rate was 47.5 MHz. Figure 1 shows the experimental setup. We added time delay τ=1/frep, where frep is the repetition frequency, to one of the two pulse trains and added another delay deltaτ for preventing optical interference. We confirmed that intensity noise of the two pulse trains colineared at a polarization beam splitter (PBS) was coincident to the SNL both before and after fiber propagation at 22MHz. SNL was measured by balanced homodyne detection. We employed nonlinear polarization interferometer to generate squeezed light[2]. For measuring photon number squeezing, a branch ratio at PBS1 and PBS3,4 was adjusted to 90:10 and 95:5, respectively. We constructed another Michelson interferometer after a beam splitter to compensate the difference of fiber length. As a result, a maximum photon-number squeezing of 2.6 dB was obtained when average power was 4mW.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)May 1, 20130 citations

\langle b(t) b(t+t')\rangle

for transmitted fields as well as

\langle b^\dagger(t) b^\dagger(t+t') b(t+t') b(t) \rangle

. We also demonstrate how

\langle b(t) b(t+t') \rangle

, a first-order correlation function, shows nonlinear photon correlations that are similar to those known and measured for two-photon scattering states. Finally, we also study the squeezed spectra of the pulse before and after interacting with the two-level system, and highlight the role of the spectral bandwidth of the incident pulse. The MPS theory allows the modeling of arbitrary bandwidth squeezing without making any Markov and Born approximations for the light-matter interaction processes, and can easily be extended to waveguide systems with multiple emitters and time-delayed feedback.