Einstein-Podolsky-Rosen Experiment with Two Bose-Einstein Condensates

In 1935, Einstein, Podolsky, and Rosen (EPR) conceived a gedanken experiment which became a cornerstone of quantum technology and still challenges our understanding of reality and locality today. While the experiment has been realized with small quantum systems, a demonstration of the EPR paradox with massive many-particle systems remains an important challenge, as such systems are particularly closely tied to the concept of local realism in our everyday experience and may serve as probes for new physics at the quantum-to-classical transition. In this work we report an EPR experiment with two spatially separated Bose-Einstein condensates, each containing about 700 rubidium atoms. Entanglement between the condensates results in strong correlations of their collective spins, allowing us to demonstrate the EPR paradox between them. Our results represent the first observation of the EPR paradox with spatially separated, massive many-particle systems. They show that the conflict between quantum mechanics and local realism does not disappear as the system size increases to more than a thousand massive particles. Furthermore, EPR entanglement in conjunction with individual manipulation of the two condensates on the quantum level, as we demonstrate here, constitutes an important resource for quantum metrology and information processing with many-particle systems.

Popular Summary

In 1935, physicists Einstein, Podolsky, and Rosen (EPR) conceived a thought experiment that revealed the conflict between quantum mechanics and our common-sense, classical understanding of locality and reality. This “EPR paradox” has also become a cornerstone of quantum technology. Although the EPR paradox has been observed with small systems composed of a few particles, how it extends into the macroscopic world remains an open question. In our experiment, we demonstrate for the first time the EPR paradox with two massive many-particle systems.

In close analogy to the original EPR thought experiment, we use atomic interactions to entangle approximately 1400 rubidium-87 atoms in a two-component Bose-Einstein condensate (BEC), which we then coherently split into two separate condensates. Our splitting technique preserves the coherence between the split BECs and allows us to individually manipulate them. The entanglement inherited from the initial state is strong enough to allow us to observe the EPR paradox between the two BECs.

Our work shows that the conflict between quantum mechanics and classical physics does not disappear when the system size is increased to more than 1000 massive particles.

Furthermore, EPR entanglement is a valuable resource for quantum technologies. For this resource to be useful, the involved systems need to be spatially separated and individually addressable on the quantum level, as we demonstrate here.

Figure 1

Schematic of an EPR experiment with two particles (left) and with two many-particle systems (right), where the spin degree of freedom is considered [39, 40]. In both cases, the particles are entangled by interactions and subsequently split into two different locations. In the case of the many-particle system, the interactions produce multipartite entanglement, which is inherited by the split systems in the form of bipartite entanglement between their collective spins.

Figure 2

Experimental sequence for spatial splitting and independent coherent control of the two condensates. (a) Space-time schematic. Orange and green color refer to condensate $A$ and $B$, respectively, whereas magenta represents the splitting pulse. Bottom left: main control parameters for splitting and state manipulation. The timing is aligned with the sketch above, but not to scale. On the right, typical absorption images are shown, from which the atom numbers in all four states are determined. This corresponds to a measurement of the selected components of the collective spins ${\widehat{\mathbf{S}}}^A$ and ${\widehat{\mathbf{S}}}^B$. (b) Hyperfine levels of the ${}^{87}\mathrm{Rb}$ ground state with transitions for coherent splitting and manipulation of ${\widehat{\mathbf{S}}}^A$ and ${\widehat{\mathbf{S}}}^B$. (c) Individual Rabi oscillations of the two collective spins after spatial splitting. Shown are the normalized spin components $n_{A,B}=(N_1^{A,B}-N_2^{A,B})/(N_1^{A,B}+N_2^{A,B})$. The discontinuity in the horizontal axis denotes a change in timescale.

Figure 3

Spin correlations between the two BECs and illustration of the inference mechanism. The gray dots are individual data points of simultaneous measurements of spin components $S_z^A$ and $S_z^B$ (left plot) and $S_y^A$ and $S_y^B$ (right plot) of the two systems. Data points for $S_y^B$ are corrected for the phase shift due to the measured trigger jitter of the microwave generator (Appendix pp5). The blue histograms are their marginal distributions, $2\sigma$ intervals are indicated by blue dotted lines. The correlations of measurement results ($2\sigma$ covariance ellipses in blue) allow one to infer measurement results of one system from the other. This reduces the variance of the prediction as shown by the histograms and the reduced $2\sigma$ intervals in red. For comparison, the $2\sigma$ variance ellipses of ideal nonentangled states with the same number of atoms are shown in yellow.

Figure 4

Individual manipulation of the two entangled BECs on the quantum level. ${\widehat{\mathbf{S}}}_B$ is rotated by an angle $\theta$ around the $x$ axis with respect to ${\widehat{\mathbf{S}}}_A$, as sketched in the inset on the top left. The red filled circles represent ${\mathcal{E}}_{\mathrm{ent}}$, red empty circles ${\mathcal{E}}_{\mathrm{EPR}}^{B\to A}$, and blue squares ${\mathcal{E}}_{\mathrm{Hei}}^A$. The EPR paradox (entanglement) is observed if ${\mathcal{E}}_{\mathrm{EPR}}^{B\to A}$ (${\mathcal{E}}_{\mathrm{ent}}$) falls below the dashed line at unity. The insets at the bottom show the spin correlations similar to Fig. 3, with ${\widehat{S}}_z$ on top and ${\widehat{S}}_y$ at the bottom, for $\theta =0$, $\pi /2$ and $\pi$.

Figure 5

Level structure of the ${}^{87}\mathrm{Rb}$ hyperfine split ground state in the linear Zeeman regime (not to scale). The color coding is consistent with Fig. 2: orange indicates system $A$, green system $B$, and magenta the splitting transitions. The desired transitions are indicated by solid lines, the undesired close-to-resonance transitions are represented by dashed lines. (a) Transitions involved in the splitting of the condensate into systems $A$ and $B$. (b) Transitions involved in driving spin rotations of ${\widehat{\mathbf{S}}}^A$ after splitting.