Time-bin-entangled photon holes

The general concept of entangled photon holes is based on a correlated absence of photon pairs in an otherwise constant optical background. Here we consider the specialized case when this background is confined to two well-defined time bins, which allows the formation of time-bin-entangled photon holes. We show that when the typical coherent-state background is replaced by a true single-photon (Fock state) background, the basic time-bin-entangled photon-hole state becomes equivalent to one of the time-bin-entangled photon-pair states. We experimentally demonstrate these ideas using a parametric down-conversion photon-pair source, linear optics, and postselection to violate a Bell inequality with time-bin-entangled photon holes.

Figure 1

Pictorial representation contrasting energy-time-entangled PDC photon-pair states [panels (a)–(c)], with energy-time EPH states [panels (d)–(f)] realized through strong two-photon absorption (TPA) [1]. By contrasting the two-photon amplitude in panel (b) vs that in panel (e), as well as that in panel (c) vs that in panel (f), it can be seen that EPHs can be thought of as the “negative image” of PDC. A description of the two kinds of two-photon amplitudes, $A_{1,2}$ and $A_{1:2}$, is found in the main text. The amplitudes have been normalized to 1 in each plot for convenience.

Figure 2

Pictorial representation contrasting time-bin-entangled PDC states [panels (a)–(c)] realized through the use of a pump Mach-Zehnder interferometer (MZ) [11, 12] with time-bin EPH states [panels (d)–(f)]. The introduction of these time-bin EPH states is the main thrust of this paper. The optical pulses on the left side of panel (d) form the background in which the time-bin EPHs will exist. These pulses can be either coherent-state pulses or nonclassical single-photon pulses as described in the text.

Figure 3

Schematic overview of our experimental method to violate Bell's inequality using time-bin EPHs in a single-photon background. The background is formed by two single photons that are displaced by ${\tau }_o$ and mixed at a 50:50 beamsplitter. Postselection at the output of a Franson interferometer realizes the time-bin EPH state in the background state given by Eq. (2). Polarization-encoding and polarizing beamsplitters (PBSs) are used to simplify the actual experiment [23].

Figure 4

Experimental apparatus used to implement the conceptual overview of Fig. 3. A PDC source provides the two background photons, and polarization-maintaining (PM) fibers are used to implement the polarization-based MZs. The phases ${\varphi }_1$ and ${\varphi }_2$ are controlled by an adjustable birefringent BBO slab and a quarter-wave plate as described in the text. Fiber polarization controllers (fpc's) are used to define and maintain the relevant polarization states, and 10-nm bandpass interference filters are used to define a PDC photon coherence time of $\sim$200 fs.

Figure 5

Experimental violation of Bell's inequality with time-bin EPHs. The solid lines are least-squares fits to the data constrained by a common period. The visibility of the black-squares curve is ($86.1\pm 0.$5)%, and the blue-triangles curve is ($81.7\pm 0.$5)%.