Attosecond Control of Squeezed Light

Abstract

Squeezed light has revolutionized quantum metrology by enhancing interferometry for sensitive applications such as the detection of gravitational waves. Squeezed light has also played a pivotal role in quantum information science with numerous applications in quantum computing and communication. Previously, squeezed light has been primarily generated using nonlinear optical interactions, where control of the degree of squeezing was possible by tuning the nonlinearity of the generating medium using suitable material engineering. Here, we modulate the third-order nonlinear response in dielectrics with strong ultrafast laser fields to control the degree of squeezing on attosecond time scales. We demonstrate the ability to change the ultrafast squeezed light generated in the nonlinear process from amplitude-squeezed to phase-squeezed by controlling the strong-field-driven nonlinear response of the material through a sub-cycle phase delay between the input femtosecond laser pulses. The squeezing of quantum noise is measured using a frequency-resolved balanced homodyne detection scheme capable of extracting the field quadratures in different frequency modes simultaneously. Using this frequency-resolved measurement we extract the complete coherency matrix containing the quantum correlations between field quadratures across different frequency modes of the femtosecond squeezed light pulse. These results have major implications for the development of quantum light sources with unprecedented levels of control over quadrature squeezing, for applications in multimode quantum information processing, and for measuring transient quantum matter correlations via transduction to quantum field correlations in an ultrafast light-matter interaction.

Figures (9)

• Figure 1: Concept and Experimental Scheme: (a) Three femtosecond pulses interact with a large band-gap dielectric (MgO) and generate a four-wave mixing signal exhibiting quadrature squeezing. The four-wave mixing process occurs simultaneously with a modulation of the material band-structure (inset in (a)) driven by the strong electric field of the laser pulses. This band modulation results in attosecond scale control of the degree and type of quadrature squeezing. The quantum state of this broadband squeezed light is measured with a frequency-resolved homodyne tomography technique revealing multi-frequency mode quadrature correlations in the generated ultrafast squeezed light. (b) shows quadrature variance modulation from theory and (c) a schematic of quadrature correlations between different frequency modes that can be extracted from the experiment.
• Figure 2: Schematic of ultrafast squeezed light generation with attosecond control and frequency-resolved balanced homodyne detection using a grating spectrometer. A 50-fs laser beam is split to form the local oscillator and a squeezed light generation beam. The squeezed light is generated using a degenerate four-wave mixing (DFWM) scheme using three beams created using a second beamsplitter and a two-hole mask. The DFWM interaction occurs in a 100 micron thick MgO target (squeezer) placed at the focus. The DFWM signal beam (squeezed light) is collimated using a lens and sent to the balanced homodyne setup, where it is combined with the local oscillator using a beamsplitter. The transmitted and reflected beams from the beamsplitter propagate to a diffraction grating, and the resulting spectra are imaged with a CMOS camera. Delay stage 1 introduces an attosecond-scale time delay ($\tau$) between the DFWM pulses for attosecond squeezing control. The phase delay ($\phi_{LO}$) between the squeezed light and the local oscillator is scanned using delay stage 2. BS: 50/50 beamsplitter.
• Figure 3: The normalized Wigner distribution function obtained from the homodyne signal for time delays (a) $\tau = 5.4$ fs and (b) $\tau = 10.2$ fs. The NRM-filtered Wigner functions are shown in (c) for $\tau = 5.4$ fs and in (d) for $\tau = 10.2$ fs. Negativity of the Wigner function is seen in (c) and (d) indicating non-classical nature of the measured light. The NRM-filtered Wigner function for 808 nm is then fitted to a 2D Gaussian function. The variances of the 2D Gaussian function are extracted using the fitting procedure for each time delay and shown in (e). The quadrature variances shown in (e) corresponding to time delays shown in (c) and (d) are indicated with red and black arrows in the Wigner plots. $X_{\theta}$ and $P_{\theta}$ are generalized quadratures. The rapidly varying and constant shot noise level (SNL) regions are separated using a blue dashed line as Region 1 and Region 2, respectively (see the main text for details). (f) shows the oscillation of the maximum and minimum variances as a function of time delay for different wavelengths within the bandwidth of the squeezed light pulse. These oscillations at different wavelengths are observed to be synchronized in-phase. The relative intensity noise (RIN) for unfiltered coherent state (magenta), NRM-filtered coherent state (green), and NRM-filtered squeezed state (blue) are obtained using the power spectral density of the homodyne signal at time delay $\tau=7.6~\mathrm{fs}$ (coherent) and $\tau=10.2~\mathrm{fs}$ (squeezed). These RIN measurements performed using the CMOS camera are shown in (g). The quadrature noise of the coherent state obtained using the homodyne signal measurement is compared with the shot noise level of the laser using standard balanced photodiode detectors, and shown in (h). The overlap of the coherent state RIN with the laser shot noise RIN in (h) shows that the coherent state RIN in (g) corresponds to the shot-noise level and that squeezing is measured below the shot-noise limit.
• Figure 4: The correlation functions (a) $\langle X_m X_n \rangle$ + $\langle P_m P_n\rangle$ and (b) $\langle X_m P_n \rangle$ - $\langle P_m X_n\rangle$ are shown, where $m$ and $n$ denote the frequency modes. Here, $X$ represents the quadrature along the direction of maximum squeezing, and $P$ is the conjugate quadrature orthogonal to $X$, evaluated for the Wigner function at $\tau = 10.2~\mathrm{fs}$. From these correlation functions, the coherency matrix is constructed (see Eq. \ref{['coherency_matrix']}). The eigenvalues of the coherency matrix, obtained via diagonalization, are shown in (c). The eigenvector corresponding to the dominant first principal mode, presented in (d), reveals that this mode constitutes a linear combination of multiple frequency components with approximately equal weights.
• Figure 5: The Wigner distributions calculated using the nonlinear Schrödinger equation (see Eq. \ref{['theory_WDF']}) are shown for different values of the dimensionless coupling constant $\bar{\chi}$ (a) $4$, (b) $2$, (c) $0$, and (d) $-4$. Panel (e) illustrates that modulation of $\bar{\chi}$ leads to corresponding modulation in the variances of the generalized quadratures. The eigenvalues of the calculated coherency matrix are shown in panel (f), indicating that the photon population is predominantly confined to the first principal mode, with only minor contributions from higher-order modes. This result is consistent with the principal mode decomposition obtained from the experimentally measured data.