Efficient simulation of ultrafast quantum nonlinear optics with matrix product states

Ultrashort pulses propagating in nonlinear nanophotonic waveguides can simultaneously leverage both temporal and spatial field confinement, promising a route towards single-photon nonlinearities in an all-photonic platform. In this multimode quantum regime, however, faithful numerical simulations of pulse dynamics naïvely require a representation of the state in an exponentially large Hilbert space. Here, we employ a time-domain, matrix product state (MPS) representation to enable efficient simulations by exploiting the entanglement structure of the system. To extract physical insight from these simulations, we develop an algorithm to unravel the MPS quantum state into constituent temporal supermodes, enabling, e.g., access to the phase-space portraits of arbitrary pulse waveforms. As a demonstration, we perform exact numerical simulations of a Kerr soliton in the quantum regime. We observe the development of non-classical Wigner-function negativity in the solitonic mode as well as quantum corrections to the semiclassical dynamics of the pulse. A similar analysis of$χ<#comment/>(2)$simultons reveals a unique entanglement structure between the fundamental and second harmonics. Our approach is also readily compatible with quantum trajectory theory, allowing full quantum treatment of propagation loss and decoherence. We expect this work to establish the MPS technique as part of a unified engineering framework for more »

Authors:
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Award ID(s):
Publication Date:
NSF-PAR ID:
10305504
Journal Name:
Optica
Volume:
8
Issue:
10
Page Range or eLocation-ID:
Article No. 1306
ISSN:
2334-2536
Publisher:
Optical Society of America
1. Electro-optic quantum coherent interfaces map the amplitude and phase of a quantum signal directly to the phase or intensity of a probe beam. At terahertz frequencies, a fundamental challenge is not only to sense such weak signals (due to a weak coupling with a probe in the near-infrared) but also to resolve them in the time domain. Cavity confinement of both light fields can increase the interaction and achieve strong coupling. Using this approach, current realizations are limited to low microwave frequencies. Alternatively, in bulk crystals, electro-optic sampling was shown to reach quantum-level sensitivity of terahertz waves. Yet, the coupling strength was extremely weak. Here, we propose an on-chip architecture that concomitantly provides subcycle temporal resolution and an extreme sensitivity to sense terahertz intracavity fields below 20 V/m. We use guided femtosecond pulses in the near-infrared and a confinement of the terahertz wave to a volume of$VTHz∼<#comment/>10−<#comment/>9(λ<#comment/>THz/2)3$in combination with ultraperformant organic molecules ($r33=170pm/V$) and accomplish a record-high single-photon electro-optic coupling rate of, 10,000 times higher than in recent reports of sensing vacuum field fluctuations in bulk media. Via homodyne detection implemented directly on chip, the interaction results into an intensity modulation of the femtosecond pulses. The single-photon cooperativity is$C0=1.6×<#comment/>10−<#comment/>8$, and the multiphoton cooperativity is$C=0.002$at room temperature. We show$><#comment/>70dB$dynamic range in intensity at 500 ms integration under irradiation with a weak coherent terahertz field. Similar devices could be employed in future measurements of quantum states in the terahertz at the standard quantum limit, or for entanglement of subsystems on subcycle temporal scales, such as terahertz and near-infrared quantum bits.
2. We demonstrate a Bell state analyzer that operates directly on frequency mismatch. Based on electro-optic modulators and Fourier-transform pulse shapers, our quantum frequency processor design implements interleaved Hadamard gates in discrete frequency modes. Experimental tests on entangled-photon inputs reveal fidelities of$∼<#comment/>98%<#comment/>$for discriminating between the$|Ψ<#comment/>+⟩<#comment/>$and$|Ψ<#comment/>−<#comment/>⟩<#comment/>$frequency-bin Bell states. Our approach resolves the tension between wavelength-multiplexed state transport and high-fidelity Bell state measurements, which typically require spectral indistinguishability.
3. The absence of the single-photon nonlinearity has been a major roadblock in developing quantum photonic circuits at optical frequencies. In this paper, we demonstrate a periodically poled thin film lithium niobate microring resonator (PPLNMR) that reaches 5,000,000%/W second-harmonic conversion efficiency—almost 20-fold enhancement over the state-of-the-art—by accessing its largest$χ<#comment/>(2)$tensor component$d33$via quasi-phase matching. The corresponding single-photon coupling rate$g/2π<#comment/>$is estimated to be 1.2 MHz, which is an important milestone as it approaches the dissipation rate$κ<#comment/>/2π<#comment/>$of best-available lithium niobate microresonators developed in the community. Using a figure of merit defined as$g/κ<#comment/>$, our device reaches a single-photon nonlinear anharmonicity approaching 1%. We show that, by further scaling of the device, it is possible to improve the single-photon anharmonicity to a regime where photon blockade effect can be manifested.
4. We perform single-shot frequency domain holography to measure the ultrafast spatio-temporal phase change induced by the optical Kerr effect and plasma in flexible Corning Willow Glass during femtosecond laser–matter interactions. We measure the nonlinear index of refraction ($n2$) to be$(3.6±<#comment/>0.1)×<#comment/>10−<#comment/>16cm2/W$and visualize the plasma formation and recombination on femtosecond time scales in a single shot. To compare with the experiment, we carry out numerical simulations by solving the nonlinear envelope equation.
5. We report on spectroscopic measurements on the$4f76s28S7/2∘<#comment/>→<#comment/>4f7(8S∘<#comment/>)6s6p(1P∘<#comment/>)8P9/2$transition in neutral europium-151 and europium-153 at 459.4 nm. The center of gravity frequencies for the 151 and 153 isotopes, reported for the first time in this paper, to our knowledge, were found to be 652,389,757.16(34) MHz and 652,386,593.2(5) MHz, respectively. The hyperfine coefficients for the$6s6p(1P∘<#comment/>)8P9/2$state were found to be$A(151)=−<#comment/>228.84(2)MHz$,$B(151)=226.9(5)MHz$and$A(153)=−<#comment/>101.87(6)MHz$,$B(153)=575.4(1.5)MHz$, which all agree with previously published results except for A(153), which shows a small discrepancy. The isotope shift is found to be 3163.8(6) MHz, which also has a discrepancy with previously published results.