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Abstract
For decades we have known that an optical parametric oscillator (OPO) generates a two-mode squeezed vacuum state. Due to the mechanics of a cavity, the parametric down-converted photons can be generated at the optical carrier frequency, or in equally-spaced side-band frequencies symmetrically above and below the carrier. These frequencies can be within the OPO linewidth centred on the carrier (spaced by kHz-MHz) or at the cavity resonances evenly spaced by the free spectral range (FSR) (spaced by MHz-GHz). The entangled photons in each correlated pair of side-bands form a two-mode squeezed vacuum state. Since the photons only differ by kHz-GHz, the output from an OPO is usually viewed as degenerate. This is due to the way a homodyne detector measures this two-mode state. Homodyne detection automatically performs a mixing operation on the side-bands which rotates the measurement basis. In this rotated basis the two-mode state becomes two separable single-mode squeezed vacua. The standard homodyne detection technique cannot distinguish between these two states. Therefore giving measurements that look like an OPO is a degenerate system which produces a single-mode squeezed vacuum state. We have shown that combining the wave-like nature of homodyne detection with the particle-like nature of photon counting in a hybrid experiment can produce an asymmetric two-mode quantum state. Applying photon-subtraction to two-mode squeezed vacua produces two single-mode states that are distinguishable: a photon-subtracted squeezed vacuum state and a squeezed vacuum state. These states cannot be properly characterized by a measurement technique that cannot distinguish between them. We applied a novel measurement that combines time-domain measurements with frequency-resolved homodyne detection for a fixed demodulation phase. The ability to control this phase gives us independent access to either single-mode state. We performed quantum state tomography on our projected state and separately reconstruct each single-mode state. We also showed that the photon-subtracted squeezed state is a quantum non-Gaussian state without homodyne detection efficiency correction by extracting entanglement between the first three FSRs created by the optical implementation of our projector. Therefore, by accessing the FSR side-band modes of a nondegenerate OPO we were able to generate both quantum Gaussian and quantum non-Gaussian states that are independent yet traveling in the same optical mode.