Balanced homodyne detection provides a phase-sensitive measurement of a quantum state. To find the variance of an arbitrary frequency dependant quadrature operator Embedded Image of the signal field, we interfered the signal beam on a 50/50 beamsplitter (BS) with a bright LO beam with a relative phase ϕ. The outputs from the BS were coupled to a pair of photodetectors, and the difference of the photocurrents was recorded. Assuming that the power of LO is much higher than that of the signal beam, the effect of LO is to rotate the coherent amplitudes of the two BS outputs, allowing measurement of an arbitrary state quadrature.

To achieve a calibrated quadrature measurement of the variance of the input state Embedded Image, we measured the variance of the difference of the BS photocurrents Vdiff and blocked the input state (but not the LO beam). In this case, it is a vacuum state entering the BS input port, and hence we can normalize the variance by assigning Vsig|blocked = 1 for any ϕ and any side-band frequency. The ratio of the variances with the input signal unblocked and blocked provided a calibrated measurement of Embedded Image, i.e., Embedded Image, where the relative phase between the signal and LO beam defines the measured quadrature. A review of this topic can be found in (40).

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