Experimental test of photonic entanglement in accelerated reference frames

Abstract

The unification of the theory of relativity and quantum mechanics is a long-standing challenge in contemporary physics. Experimental techniques in quantum optics have only recently reached the maturity required for the investigation of quantum systems under the influence of non-inertial motion, such as being held at rest in gravitational fields, or subjected to uniform accelerations. Here, we report on experiments in which a genuine quantum state of an entangled photon pair is exposed to a series of different accelerations. We measure an entanglement witness for g-values ranging from 30 mg to up to 30 g-under free-fall as well on a spinning centrifuge-and have thus derived an upper bound on the effects of uniform acceleration on photonic entanglement.

Figure 1. Sketch of the source crate.

(b) A laser diode pumps a ppKTP crystal heated by an oven, generating photon pairs collected in a polarization maintaining single-mode fibre. An additional Nd:YVO₄ crystal is used to fine-tune the walk-off compensation. A BS creates an equal superposition for reflection and transmission for each individual photon, which leads to an polarization-entangled state in postselection. Using various half- and quarter-wave plates (HWP, QWP) and PBS, the polarization correlations can be analysed in different measurement bases and measured in detectors (D1,D2,D3 and D4). (a) Source (level 1), electronics (level 2), as well as polarization analysis and detection module (level 3) are placed at different levels inside the crate and thus exhibit different maximal g-values.

Figure 2. Scheme of the experiments.

(a) The crate was dropped from 12 m for a low-g (almost) free-fall flight in air of 1.4 s. A 1.3-m-high stack of mattresses was used to reduce deceleration on impact (Supplementary Movie 1). (b) The source crate was installed in one of the centrifuge gondolas at a distance of about 3 m from the axis, at full speed. The orientation of the accelerometer reference frame are shown when the centrifuge is at rest and in motion (Supplementary Movie 2).

Figure 3. Data for drop tower experiment.

(A) Elapsed time at rest, (B) free-fall flight (C) and after impact versus HV- (left) and DA-visibility (right) measured in 500 ms slots compared to its average (denoted as horizontal dashed line). Each of data points shown consists of ≈3,500 coincident counts and V_DA=96% on average. The error bars shown in the graphs are calculated considering Poissonian statistics, as well as systematical errors for DA measurements due to temperature fluctuations. The actual g-value shows the drag from contacts with the guiding rail and the wind at higher velocities. The impact (at 1.45 s) consisted of a 16 g deceleration phase (g-sensor saturated) and a rebound phase (at 2 s).

Figure 4. Data from centrifuge experiment.

Time elapsed versus g-force and visibility in the DA (triangles) and HV (circles) polarization measurement basis. The average of the visibilities is represented as horizontal dashed line (94.8 and 98.3%). Each of the points was calculated from ≈14,000 coincident counts. The error bars shown in the graphs are calculated considering Poissonian statistics, as well as systematical errors for DA measurements due to temperature fluctuations. The drop in visibility at 15 g is due to the effective cooling of the crystal during higher angular spinning speeds. The lower g-values (light blue) represent the measured data of the g-sensor at level 3 (detection) of the crate. In addition the calculated acceleration at level 1 (source) is plotted (blue).

Figure 5. Summary of experimental data.

All data acquired during the experiments shown as the g-value versus lower bound on Bell-state fidelity , for g-values ranging from 3 mg to up to 30 g. The error bars shown in the graphs are calculated considering Poissonian statistics, as well as systematical errors for DA measurements due to temperature fluctuations. No deviation from the total average (96.45% represented as horizontal dashed line) for more than the estimated errors is visible.