Pulsed homodyne tomography of highly nonclassical states of the light field

PULSED OPTICAL HOMODYNE TOMOGRAPHY OF HIGHLY NON-CLASSICAL STATES OF THE LIGHT FIELD Quantum state reconstruction using optical homodyne tomography has been established as a reliable technique to obtain full information about quantum states of the light field [1]. We have extended our experience in tomographic reconstruction of cw-field states [2] to pulsed states of the light field. Pulsed optical homodyne tomography has formerly been applied to coherent and squeezed states by the group of M.G. Raymer [3]. We have advanced this technique to highly non-classical states such as the single-photon state. The single photon Fock state is one of the most fundamental states of the light field. It is highly non-classical and reveals the particle aspect of the quantized light field most strikingly. We have performed quantum state reconstruction of pulsed single-photon Fock states with measurement efficiencies of up to 33% at the time of submitting this abstract. As a result, non-Gaussian marginal distributions of optical quantum states are measured for the first time. From these data non-Gaussian (exhibiting a central dip) Wigner functions have been reconstructed. This study combines the techniques of photon counting and homodyne detection for the first time in a single experiment. In our experimental setup we employ a mode-locked Ti:Sapphire-laser in combination with a pulse picker to obtain transform limited picosecond pulses at 790 nm. Most of the radiation is single-pass frequency doubled in a BBO-crystal yielding 50 uW at 395 nm, which is then passed on to a BBO-crystal cut for Type I down-conversion. The down-converter is operated in a frequency degenerate, but spatially non-degenerate configuration yielding up to 1000 photon pairs per second. A single photon counter is placed in one of the emission channels - labeled trigger - to detect photon pair creation events and to trigger the readout of a homodyne system placed in the other emission channel - labeled signal. This way we select for the homodyne measurements only those pulses where a photon has been emitted into the signal channel, thus conditionally preparing single photon Fock states. A small fraction of the original optical pulses from the pulse picker is used as local oscillator for the homodyne system. These pulses have to be temporally and spatially mode-matched to the mode of the photons in the signal channel. In order to be able to detect the quantum noise of single photons at the pulse picking rate, we have designed a homodyne system with ultra-low electronic noise (500 electrons per pulse) and high subtraction efficiency (> 83 dB). The phase-independent marginal distribution of the prepared state is obtained as the statistical distribution of the homodyne measurement output. Inverse Radon transformation is then used to reconstruct the Wigner function from the measured marginal distribution. As an outlook, we propose to employ the developed method to study more complex non-classical states of the light field with the ultimate goal of being able to synthesize arbitrary light field states. Simple extensions of the existing setup will allow us to produce photon-added states and displaced Fock states. As the next step, we propose to employ a novel scheme of repeated two-photon down-conversion to produce higher Fock states. In this scheme, the photons emitted into the signal mode are repeatedly fed back into the down converter. The desired state is prepared conditioned on the readout of the monitor detector in the idler channel. Employing either a seed beam in the idler path or a high transmission beam splitter in the signal path it becomes possible to add coherent displacements to the constructed states so that arbitrary truncated field states can be achieved.