Observation of squeezed states with strong photon-number oscillations

Squeezed states of light constitute an important nonclassical resource in the field of high-precision measurements, for example, gravitational wave detection, as well as in the field of quantum information, for example, for teleportation, quantum cryptography, and distribution of entanglement in quantum computation networks. Strong squeezing in combination with high purity, high bandwidth, and high spatial mode quality is desirable in order to achieve significantly improved performances contrasting any classical protocols. Here we report on the observation of 11.5 dB of squeezing, together with relatively high state purity corresponding to a vacuum contribution of less than 5%, and a squeezing bandwidth of about 170 MHz. The analysis of our squeezed states reveals a significant production of higher-order pairs of quantum-correlated photons and the existence of strong photon-number oscillations.

Figure 1

Experimental apparatus. (a) Schematic diagram of the experimental setup. A small part of the 1064-nm output of the 2-W laser system was used as local oscillator while the majority was sent to an external second-harmonic generation (SHG) cavity which provided the 532-nm pump beam to drive the OPO. Travelling wave filter cavities (FC1064 and FC532) in both paths were used to provide stable and well-defined laser beams. Squeezed vacuum states at 1064 nm were generated by type I OPO below threshold in a nonlinear monolithic cavity. A balanced homodyne detector was used to measure the states’ quadrature variances. DBS, dichroic beam splitter; PD, photo diode; SA, spectrum analyzer. (b) Exploded assembly drawing of the oven enclosing the squeezed light source. The nonlinear crystal, copper plates, Peltier elements, and thermal insulations are shown. The inlay shows a photograph of the monolithic squeezed light source made from 7% doped MgO:LiNbO${}_3$.

Figure 2

Quadrature noise variances as measured by balanced homodyne detection of three different states produced by the OPO. All traces were recorded at a Fourier frequency of $f=5$ MHz, with a resolution bandwidth of $\Delta f=100$ kHz and a video bandwidth of 100 Hz, and were normalized to the vacuum noise. The data still include electronic detector dark noise; hence all traces represent direct observations without any data postprocessing. (a) Squeezed vacuum state that was generated with a second-harmonic pump power of $P_{\mathrm{sh}}=30$ mW. A nonclassical noise reduction of 2.9 dB below vacuum noise was observed, with the respective antisqueezing of 2.9 dB above shot noise. (b) Squeezed vacuum state generated with an increased pump power of $P_{\mathrm{sh}}=150$ mW. Squeezing of 6.2 dB was measured with 6.7 dB of antisqueezing. (c) Driving the OPO at maximum pump power $P_{\mathrm{sh}}=600$ mW yielded squeezing and antisqueezing of 11.5 and 16.0 dB, respectively. The subtraction of the detector dark noise would further increase the value of maximum squeezing to 11.6 dB.

Figure 3

Wigner function of the squeezed vacuum state produced by our OPO. The projections (solid curves) onto the two quadratures yield the Gaussian probability distributions with variances of $-$11.5 and 16 dB relative to the projections belonging to a pure vacuum state (dotted curves).

Figure 4

Density matrix of the squeezed state of Fig. 2c. Plot of the absolute values of the density matrix elements with photon numbers up to 10 for the $-$11.5-dB squeezed and 16-dB antisqueezed state. The diagonal elements give the probabilities of finding $0,1,2,\dots ,n$ photons. Due to the state’s high purity, the probabilities for finding an odd number of photons is significantly suppressed.

Figure 5

Photon-number oscillation. The probability $P(n)$ of detecting $n$ photons is plotted for the squeezed vacuum states from Figs. 2a, 2b, and 2c. The photon-number distributions clearly show oscillatory behavior. With increasing squeezing the number of higher-order photon pairs grows. For clarity the inset shows a zoomed view restricted to probabilities up to 0.1.

Figure 6

High-bandwidth squeezing spectrum. Squeezing (bottom trace) and antisqueezing (top trace) are shown relative to the vacuum noise variance. The measurements were performed from 5 to 100 MHz. This was limited by the fact that the dark noise clearance of the homodyne detector was too low toward higher frequencies. The traces are averages of three measurements each done with a resolution bandwidth of 1 MHz and a video bandwidth of 3 kHz. The data were fitted to a model and revealed a squeezing bandwidth of 170 MHz (thin line).