## Abstract

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.

Original language | English (US) |
---|---|

Article number | 240401 |

Journal | Physical review letters |

Volume | 119 |

Issue number | 24 |

DOIs | |

State | Published - Dec 13 2017 |

## ASJC Scopus subject areas

- Physics and Astronomy(all)

## Access to Document

## Fingerprint Dive into the research topics of 'Spin Entanglement Witness for Quantum Gravity'. Together they form a unique fingerprint.

## Cite this

- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver

*Physical review letters*,

*119*(24), [240401]. https://doi.org/10.1103/PhysRevLett.119.240401

**Spin Entanglement Witness for Quantum Gravity**. In: Physical review letters. 2017 ; Vol. 119, No. 24.

}

*Physical review letters*, vol. 119, no. 24, 240401. https://doi.org/10.1103/PhysRevLett.119.240401

**Spin Entanglement Witness for Quantum Gravity.** / Bose, Sougato; Mazumdar, Anupam; Morley, Gavin W.; Ulbricht, Hendrik; Toroš, Marko; Paternostro, Mauro; Geraci, Andrew A.; Barker, Peter F.; Kim, M. S.; Milburn, Gerard.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Spin Entanglement Witness for Quantum Gravity

AU - Bose, Sougato

AU - Mazumdar, Anupam

AU - Morley, Gavin W.

AU - Ulbricht, Hendrik

AU - Toroš, Marko

AU - Paternostro, Mauro

AU - Geraci, Andrew A.

AU - Barker, Peter F.

AU - Kim, M. S.

AU - Milburn, Gerard

N1 - Funding Information: Bose Sougato 1 Mazumdar Anupam 2 Morley Gavin W. 3 Ulbricht Hendrik 4 Toroš Marko 4 Paternostro Mauro 5 Geraci Andrew A. 6 Barker Peter F. 1 Kim M. S. 7 Milburn Gerard 7,8 Department of Physics and Astronomy, 1 University College London , Gower Street, WC1E 6BT London, United Kingdom 2 Van Swinderen Institute University of Groningen , 9747 AG Groningen, The Netherlands Department of Physics, 3 University of Warwick , Gibbet Hill Road, Coventry CV4 7AL, United Kingdom Department of Physics and Astronomy, 4 University of Southampton , SO17 1BJ Southampton, United Kingdom CTAMOP, School of Mathematics and Physics, 5 Queen’s University Belfast , BT7 1NN Belfast, United Kingdom Department of Physics, 6 University of Nevada , Reno, 89557 Nevada, USA QOLS, 7 Blackett Laboratory , Imperial College, London SW7 2AZ, United Kingdom Centre for Engineered Quantum Systems, School of Mathematics and Physics, 8 The University of Queensland , QLD 4072, Australia 13 December 2017 15 December 2017 119 24 240401 6 September 2017 6 November 2017 © 2017 American Physical Society 2017 American Physical Society Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements. Leverhulme Trust http://dx.doi.org/10.13039/501100000275 http://sws.geonames.org/2635167/ RPG-2016-046 RPG-2014-055 National Science Foundation http://dx.doi.org/10.13039/100000001 NSF http://sws.geonames.org/6252001/ NSF PHY-1506431 Royal Society http://dx.doi.org/10.13039/501100000288 http://sws.geonames.org/2635167/ Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 EPSRC http://sws.geonames.org/2635167/ EPSRC-GB EP/K034480/1 EP/M013243/1 EP/N031105/1 EP/K004077/1 EU Collaborative Project 618074 Science Foundation Ireland http://dx.doi.org/10.13039/501100001602 SFI http://sws.geonames.org/2963597/ 15/IA/2864 European Cooperation in Science and Technology http://dx.doi.org/10.13039/501100000921 COST http://sws.geonames.org/6695072/ CA15220 H2020 European Research Council http://dx.doi.org/10.13039/100010663 H2020 Excellent Science - European Research Council European Research Council ERC http://sws.geonames.org/6695072/ 308253 marker SYNOPSIS Quantizing gravity is one of the most intensively pursued areas of physics [1,2] . However, the lack of empirical evidence for quantum aspects of gravity has lead to a debate on whether gravity is a quantum entity. This debate includes a significant community who subscribe to the breakdown of quantum mechanics itself at scales macroscopic enough to produce prominent gravitational effects [3–7] , so that gravity need not be a quantized field in the usual sense. Indeed it is quite possible to treat gravity as a classical agent at the cost of including additional stochastic noise [8–11] . Moreover, oft-cited necessities for quantum gravity (e.g., the big bang singularity) can be averted by modifying the Einstein action such that gravity becomes weaker at short distances and small time scales [12] . Thus it is crucial to test whether fundamentally gravity is a quantum entity. Proposed tests of this question have traditionally focused on specific models, phenomenology, and cosmological observations (e.g., [2,13–16] ) but are yet to provide conclusive evidence. More recently, the idea of laboratory probes (proposed originally by Bronstein [17,18] and Feynman [19] ) that emphasize the interaction of a probe mass with the gravitational field created by another mass [20–25] , has started to take hold. However, this approach does not yet clarify how the possible quantum coherent nature of gravity can be unambiguously certified in an experiment. In this Letter, we present the scheme for an experiment that not only would certify the potential quantum coherent behavior of gravity, but would also offer a much more prominent witness of quantum gravity than existing laboratory-based proposals. We show that the growth of entanglement between two mesoscopic test masses in adjacent matter-wave interferometers [Fig. 1(b) ] can be used to certify the quantum character of the mediator (gravitons) of the gravitational interaction—in the same spirit as a Bell inequality certifies the “nonlocal” character of quantum mechanics. We make two striking observations that make the test for quantum gravity accessible with feasible advances in interferometry: (i) For mesoscopic test masses ∼ 10 - 14 kg (with which interference experiments might soon be possible [26] ) separated by ∼ 100 μ m , the quantum mechanical phase E τ / ℏ induced by their gravitational interaction (with E being their gravitational interaction energy, and τ ∼ 1 s their interaction time) is significant enough to generate an observable entanglement between the masses; (ii) if we use test masses with embedded spins and a Stern-Gerlach scheme [27,28] to implement our interferometry, then, at the end of the interferometry, the gravitational interaction of the test masses actually entangles their spins which are readily measured in complementary bases (necessary in order to witness entanglement). Additionally, although our approach is independent of the specifics of any quantum theory of gravity (in the same spirit as using entanglement to study the nature of unknown processes [29,30] ), we show, in Supplemental Material [31] , that off-diagonal terms between coherent states (a signature of the quantum superposition principle) of the Newtonian gravitational field are necessary for the development of the entanglement between the test masses. 1 10.1103/PhysRevLett.119.240401.f1 FIG. 1. Adjacent interferometers to test the quantum nature of gravity: (a) Two test masses held adjacently in superposition of spatially localized states | L ⟩ and | R ⟩ . (b) Adjacent Stern-Gerlach (SG) interferometers in which initial motional states | C ⟩ j of masses are split in a spin dependent manner to prepare states | L , ↑ ⟩ j + | R , ↓ ⟩ j ( j = 1 , 2). Evolution under mutual gravitational interaction for a time τ entangles the test masses by imparting appropriate phases to the components of the superposition. This entanglement can only result from the exchange of quantum mediators—if all interactions aside gravity are absent, then this must be the gravitational field (labeled h 00 where h μ ν are weak perturbations on the flat space-time metric η μ ν ). This entanglement between test masses evidencing quantized gravity can be verified by completing each interferometer and measuring spin correlations. Our proposal relies on two simple assumptions: (a) the gravitational interaction between two masses is mediated by a gravitational field (in other words, it is not a direct interaction at a distance) and (b) the validity of a central principle of quantum information theory: entanglement between two systems cannot be created by local operations and classical communication (LOCC) [38] . It can readily be proved that, in the absence of closed timelike loops [39] (i.e., under the assumption of validity of the chronology protection conjecture [40] ) and as long as the notion of classicality itself is not extended significantly [41] , LOCC keeps any initially unentangled state separable. Translating to our setting of two test masses in adjacent interferometers any external fields (including the gravitational fields from other masses around them) can only make LOs on their states, while a classical gravitational field propagating between the test masses can only give a CC channel between them. These LOCC processes cannot entangle the states of the masses. Thus it immediately follows that if the mutual gravitational interaction entangles the state of two masses, then the mediating gravitational field is necessarily quantum mechanical in nature. Entanglement due to gravitational interaction.— We first consider a schematic version that clarifies how the states of two neutral test masses 1 and 2 (masses m 1 and m 2 ), each held steadily in a superposition of two spatially separated states | L ⟩ and | R ⟩ as shown in Fig. 1(a) for a time τ , get entangled. Imagine the centers of | L ⟩ and | R ⟩ to be separated by a distance Δ x , while each of the states | L ⟩ and | R ⟩ is a localized Gaussian wave packet with widths ≪ Δ x so that we can assume ⟨ L | R ⟩ = 0 . There is a separation d between the centers of the superpositions as shown in Fig. 1(a) so that even for the closest approach of the masses ( d - Δ x ), the short-range Casimir-Polder force is negligible. Distinct components of the superposition have distinct gravitational interaction energies as the masses are separated by different distances and thereby have different rates of phase evolution. Under these circumstances, the time evolution of the joint state of the two masses is purely due to their mutual gravitational interaction, and given by | Ψ ( t = 0 ) ⟩ 12 = 1 2 ( | L ⟩ 1 + | R ⟩ 1 ) 1 2 ( | L ⟩ 2 + | R ⟩ 2 ) (1) → | Ψ ( t = τ ) ⟩ 12 = e i ϕ 2 { | L ⟩ 1 1 2 ( | L ⟩ 2 + e i Δ ϕ L R | R ⟩ 2 ) + | R ⟩ 1 1 2 ( e i Δ ϕ R L | L ⟩ 2 + | R ⟩ 2 ) } , (2) where Δ ϕ R L = ϕ R L - ϕ , Δ ϕ L R = ϕ L R - ϕ , and ϕ R L ∼ G m 1 m 2 τ ℏ ( d - Δ x ) , ϕ L R ∼ G m 1 m 2 τ ℏ ( d + Δ x ) , ϕ ∼ G m 1 m 2 τ ℏ d . One can now think of each mass as an effective “orbital qubit” with its two states being the spatial states | L ⟩ and | R ⟩ , which we can call orbital states. As long as 1 / 2 ( | L ⟩ 2 + e i Δ ϕ L R | R ⟩ 2 ) and 1 / 2 ( e i Δ ϕ R L | L ⟩ 2 + | R ⟩ 2 ) are not the same state (which is very generic, happening for any Δ ϕ L R + Δ ϕ R L ≠ 2 n π , with integral n ), it is clear that the state | Ψ ( t = τ ) ⟩ 12 cannot be factorized and is thereby an entangled state of the two orbital qubits. Witnessing this entanglement then suffices to prove that a quantum field must have mediated the gravitational interaction between them. It makes sense to start with particles of the largest possible masses, namely, m 1 ∼ m 2 ∼ 10 - 14 kg for which there have already been realistic proposals for creating superpositions of spatially separated states such as | L ⟩ and | R ⟩ [26] . Note that we are constrained to design an experiment in which only the gravitational interaction is active. This means that the allowed distance of closest approach is d - Δ x ≈ 200 μ m , which is the distance at which the Casimir-Polder interaction [42] ∼ 1 / ( 4 π ε 0 ) 2 [ 23 ℏ c R 6 / 4 π ( d - Δ x ) 7 ] ( ε - 1 / ε + 2 ) 2 ∼ 0.1 of the gravitational potential, where, to take an explicit material, we have assumed R ∼ 1 μ m radius diamond microspheres with dielectric constant ε ∼ 5.7 . Note that we can get ϕ R L ∼ G m 1 m 2 τ ℏ ( d - Δ x ) ∼ O ( 1 ) (3) if the duration for which we can hold the superposition without decoherence is τ ∼ 2 s . Such a significant phase accumulation leads to a significant entanglement between the masses as the entanglement increases monotonically over Δ ϕ L R + Δ ϕ R L evolving from 0 to π and reaches maximal value for π . In practice, it is very difficult to witness directly the entanglement between the dichotomized spatial orbital degrees of freedom (d.o.f.) as generated above as, for that, one needs to measure the spatial d.o.f. in more than one spatial basis (which involves constructing ideal two port beam splitters for massive objects). We next show how we naturally solve this problem by resorting to SG interferometry, which has recently been achieved with neutral atoms [28] , and proposed for freely propagating nanocrystals with embedded spins [27] . Gravitational entanglement witnessing in SG interferometry.— The SG interferometry [cf., Fig. 1(b) ] includes the following three steps: Step 1: A spin dependent spatial splitting of the center of mass state of a test mass m j in an inhomogeneous magnetic field depicted by the evolution | C ⟩ j 1 2 ( | ↑ ⟩ j + | ↓ ⟩ j ) → 1 2 ( | L , ↑ ⟩ j + | R , ↓ ⟩ j ) , (4) where | C ⟩ is the initial localized state of m j at the center of the axis of the SG apparatus and | L ⟩ and | R ⟩ are separated states localized on its opposite sides along the axis (these are qualitatively the same ones as shown in Fig. 1 ). Step 2: “Holding” the coherent superposition created above [Eq. (4) for a time τ ; consider the magnetic field of the SG effectively switched off for a duration τ ). Step 3: The third and final step brings back the superposition through the unitary transformations | L , ↑ ⟩ j → | C , ↑ ⟩ j , | R , ↓ ⟩ j → | C , ↓ ⟩ j , (5) which is, essentially, a refocusing SG apparatus with magnetic field homogeneity oriented oppositely to the apparatus in step 1 (although, in practice, it is best to keep the same magnetic field inhomogeneity and simply flip the spin so as to reverse the SG effect of step 1). Let us now assume that two such SG interferometers with neutral test masses m 1 and m 2 operate in close proximity (but masses do not come so close as to have a significant Casimir-Polder interaction) as depicted in Fig. 1(b) . Moreover, we assume temporarily that the evolution time in steps 1 and 3 (when the spin dependent splitting and recombination takes place) is much smaller than the time needed for the accumulation of a non-negligible gravitational phase. Then during step 2 of the SG interferometry, due to the mutual gravitational interaction, the joint state of the two test masses evolves exactly as in Eq. (1) to Eq. (2) with the orbital qubit states | L ⟩ j and | R ⟩ j replaced by “spin-orbital” qubit states | L , ↑ ⟩ j and | R , ↓ ⟩ j . When we follow up the evolution of Eq. (2) of spin-orbital qubits with step 3 of Eq. (5) , then we obtain the state at the end of the SG interferometry to be | Ψ ( t = t end ) ⟩ 12 = 1 2 { | ↑ ⟩ 1 1 2 ( | ↑ ⟩ 2 + e i Δ ϕ L R | ↓ ⟩ 2 ) + | ↓ ⟩ 1 1 2 ( e i Δ ϕ R L | ↑ ⟩ 2 + | ↓ ⟩ 2 ) } | C ⟩ 1 | C ⟩ 2 , where the unimportant overall phase factor outside the state has been omitted. The above is manifestly an entangled state of the spins of the two test masses. It can be verified by measuring the spin correlations in two complementary bases in order to estimate the entanglement witness W = | ⟨ σ x ( 1 ) ⊗ σ z ( 2 ) ⟩ + ⟨ σ y ( 1 ) ⊗ σ y ( 2 ) ⟩ | . If W is found to exceed unity then the state is proven to be entangled, and, thereby, the mediator, the gravitational field, a quantum entity. An explicit scheme.— We now outline an explicit interferometer. Each SG interferometer has to be fed in by neutral masses with an embedded electronic spin, a very low internal crystal temperature, and operate under very low ambient pressure (the latter two conditions are required for suppressing decoherence over relevant time scales as described in Supplemental Material [31] ). We assume a scenario where they are released simultaneously from two adjacent traps separated by d ∼ 450 μ m , and fall vertically through their respective interferometers [27,43] . Microdiamonds with an embedded nitrogen-vacancy center spin are one candidate for the test masses—they can be trapped in diamagnetic traps [44] and cryogenically cooled. Alternatively objects such as Yb microcrystals with a single doped atomic two-level system in optical traps can be cooled in their internal temperature by laser refrigeration. Any charges should be neutralized immediately following their release from their traps by demonstrated means [45] . The core aim is to drop two objects simultaneously—one through each interferometer—so that their states can become entangled through their mutual gravitational interaction while they traverse their respective interferometers. To this end, we adopt, in each interferometer, a modified version of the SG interferometry scheme of Ref. [27] for splitting into two parts and then recombining the wave packet of each mass in the horizontal direction while they fall vertically through the interferometer. In step 1 of the SG interferometer described schematically by Eq. (4) , the test masses are subjected to an inhomogeneous magnetic field gradient in the horizontal direction for a time τ acc with a spin flip (by a short microwave π / 2 pulse) exactly midway at time τ acc / 2 . Thus the initial state of each mass (say, a Gaussian wave packet just below their respective trap location) is subjected to a spin dependent acceleration and deceleration in sequence to reach at time τ acc a superposition of spatially separated states | L , ↑ ⟩ j and | R , ↓ ⟩ j centered at x j , L and x j , R , respectively, with a spatial separation of Δ x = | x j , L - x j , R | ∼ 1 2 g μ B ∂ x B m j τ acc 2 , (6) where μ B is the Bohr magneton, g ∼ 2 the electronic g -factor, and ∂ x B the field gradient in the horizontal ( x ) direction. For a microobject of mass m ∼ 10 - 14 kg , a magnetic field gradient of ∼ 10 6 T m − 1 [27] and a time τ acc ∼ 500 ms , Δ x ∼ 250 μ m . At this stage, step 2 is carried out: A microwave pulse is used to swap the electronic state to the nuclear spin state, so that the masses are not subjected to spin dependent forces any more, and evolve by falling in parallel next to each other for a time τ . If we allow only a time of τ ∼ 2.5 s for this step, then the masses continue to fall parallel to each other to a very good approximation: their movement towards each other due to their gravitational acceleration towards each other G m / ( d - Δ x ) 2 ∼ 10 - 16 ms − 2 is truly negligible. Under these circumstances, given the different steady separations | x 1 , ξ - x 2 , ξ ′ | (where ξ , ξ ′ ∈ { L , R } ) the phases Δ ϕ L R ∼ - 0.2 and Δ ϕ R L ∼ 0.7 accumulated due to the gravitational interaction over the time τ ∼ 2.5 s . This phase accumulation alone gives W ∼ 1.16 implying a gravitationally mediated spin entanglement (the strength of the direct spin-spin dipolar interaction is ∼ 10 - 8 Hz , so that it hardly entangles the spins in the time scale of the experiment). In practice, the witness gives a larger value as phase accumulation and the adjoining entanglement growth happens also during steps 1 and 3 of the SG interferometry. A discussion of how to overcome the challenges of large superpositions necessarily accompanying our scheme, as well as the efficacy of the scheme when the scale of superpositions is smaller, is presented in Supplemental Material [31] . Decoherence.— We require both the orbital and spin d.o.f. of the masses to remain coherent for the whole duration of the experiment. As we map to nuclear spins for step 2 of the interferometry with their very long coherence times, we only require electronic spins coherent for 1 s (in steps 1 and 3), which should be possible for microdiamond below 77 K [46] with dynamical decoupling pulses on its spin bath [47] . To estimate collisional and thermal decoherence times [48–50] of the orbital d.o.f. we consider the pressure P = 10 - 15 Pa and the temperature 0.15 K: the collisional decoherence time for a superposition size of Δ x ∼ 250 μ m is the same order of magnitude as the total microsphere’s fall time τ + 2 τ acc ∼ 3.5 s , while the thermal decoherence mechanism, due to scattering, emission, and absorption of environmental photons, is negligible. Note that speculated spontaneous collapse mechanisms [4–6] , if true, typically lead to a strong loss of coherence on the time scale of the experiment and inhibit the gravitationally mediated entanglement. A pivotally important stage preceding the entangling experiment is to take the interferometers far apart from each other to characterize the relative phases between the two paths in each SG interferometer as affected by nearby surfaces, other masses, etc. While these are LO and thereby cannot give spurious entanglement between the test masses, the spin operators used in witness W have to be readjusted in accordance to these local phases. Note that although the internal cooling is necessary, the center of mass motion of the test masses, if originally released from ∼ 1 MHz traps, is allowed to have a temperature as high as 100 K as that causes only a factor of ∼ 10 - 2 change in the gravitational phase, while the change due to spreading of the wave packet during the experiment is truly negligible. Summary.— While gravity is one of the fundamental forces, its weakness has made it difficult to test theories on its nature. In particular, in order to treat gravity in the context of quantum mechanics, it is important to answer the following question: is gravity a quantum entity? Lack of a scheme to test this question has been a longstanding issue. In this Letter, based on the principle that classical mediators cannot entangle [38] , we introduce an idea to solve this problem: to observe the entanglement of two test masses to ascertain whether the gravitational field is a quantum entity (recently, we became aware of a related parallel independent work [51] ). In regard to “which” quantum aspect, the discussion in Supplemental Material [31] indicates that it should be that the gravitational field obeys the principle of quantum superposition. Instead of using the gravity of one test mass to change the position of another [20–22,52,53] , which is a tiny effect to measure for a test mass as small as those for which large quantum superpositions are feasible, we consider a change of the phase affected by the gravitational interaction, which we find to be much larger. The test described here is several orders of magnitude stronger than other predictions in the low-energy long-distance sector of quantum gravity such as post-Newtonian corrections [54,55] and decoherence induced by the gravitational field background [56–58] . Moreover, its prominence stems from a very simple and aesthetically beautiful fact: a Planck’s constant in the denominator fighting with the gravitational constant in the numerator of a relevant phase factor. The prescriptions we have provided for overcoming the challenges set out a roadmap towards quantum gravity experiments and could have other beneficial spin-offs on the way, such as the measurement of the Newtonian potential for microspheres, given that so far it has only been measured for much larger masses (this only needs one interferometer and a proximal mass) [52] . Thus the idea and scheme presented in this Letter arguably opens up the shortest route known to date for establishing the quantum nature of gravity through a laboratory experiment. Significant progress on the work took place during the KIAS workshop on “Nonclassicalities in Macroscopic Systems.” This work was presented in the ECT workshop on “Testing the limits of the quantum superposition principle,” the Benasque workshop on “Quantum Engineering of Levitated Systems,” the ICTS Bangalore discussion meeting on “Fundamental Problems of Quantum Physics,” and Quantum 2017, Torino, where feedback received from participants has been greatly beneficial. Particularly we acknowledge incisive comments and questions by Miles Blencowe, Andrew Greentree, Jonathan Oppenheim, Anis Rahman, Lorenzo Maccone, Jack Harris, Gavin Brennen, Albert Roura, Michael Hall and Dipankar Home. H. U. and M. T. acknowledge funding by the Leverhulme Trust (Grant No. RPG-2016-046) and the Foundational Questions Institute (FQXi). A. G. is supported by the U.S. National Science Foundation (Grant No. PHY-1506431). M. S. K. acknowledges a Leverhulme Trust Research Grant (Grant No. RPG-2014-055), the Royal Society, and an EPSRC grant (Grant No. EP/K034480/1). M. P. acknowledges support from the EU Collaborative Project TherMiQ (Grant No. 618074), the SFI-DfE Investigator Program (Grant No. 15/IA/2864), the Royal Society, and the COST Action CA15220 Quantum Technologies in Space. G. W. M. is supported by the Royal Society and the United Kingdom EPSRC Networked Quantum Information Technology Hub (Grant No. EP/M013243/1). P. B. and S. B. acknowledge EPSRC Grant No. EP/N031105/1. S. B. acknowledges ERC Grant No. 308253 PACOMANEDIA and EPSRC Grant No. EP/K004077/1. [1] 1 Approaches to Quantum Gravity , edited by D. Oriti ( Cambridge University Press , Cambridge, 2009 ). [2] 2 C. Kiefer , Ann. Phys. (Amsterdam) 15 , 129 ( 2006 ). APNYA6 0003-4916 10.1002/andp.200510175 [3] 3 F. Karolyhazy , Nuovo Cimento A 42 , 390 ( 1966 ). NCIAAT 0369-3546 10.1007/BF02717926 [4] 4 R. Penrose , Gen. Relativ. Gravit. 28 , 581 ( 1996 ). GRGVA8 0001-7701 10.1007/BF02105068 [5] 5 L. Diosi , Phys. Rev. A 40 , 1165 ( 1989 ). PLRAAN 0556-2791 10.1103/PhysRevA.40.1165 [6] 6 A. Bassi , K. Lochan , S. Satin , T. P. Singh , and H. Ulbricht , Rev. Mod. Phys. 85 , 471 ( 2013 ). RMPHAT 0034-6861 10.1103/RevModPhys.85.471 [7] 7 A. Bassi , A. Grossart , and H. Ulbricht , Classical Quantum Gravity 34 , 193002 ( 2017 ). CQGRDG 0264-9381 10.1088/1361-6382/aa864f [8] 8 D. Kafri , J. M. Taylor , and G. J. Milburn , New J. Phys. 16 , 065020 ( 2014 ). NJOPFM 1367-2630 10.1088/1367-2630/16/6/065020 [9] 9 D. Kafri and J. M. Taylor , arXiv:1311.4558 . [10] 10 A. Tilloy and L. Diósi , Phys. Rev. D 93 , 024026 ( 2016 ). PRVDAQ 2470-0010 10.1103/PhysRevD.93.024026 [11] 11 A. Tilloy and L. Diósi , arXiv:1706.01856 . [12] 12 T. Biswas , E. Gerwick , T. Koivisto , and A. Mazumdar , Phys. Rev. Lett. 108 , 031101 ( 2012 ). PRLTAO 0031-9007 10.1103/PhysRevLett.108.031101 [13] 13 S. Hossenfelder , Classical Quantum Gravity: Theory, Analysis and Applications , edited by V. R. Frignanni ( Nova Publishers , 2011 ), Chap. 5. [14] 14 Amjad Ashoorioon , P. S. Bhupal Dev , and A. Mazumdar , Mod. Phys. Lett. A 29 , 1450163 ( 2014 ). MPLAEQ 0217-7323 10.1142/S0217732314501636 [15] 15 I. Pikovski , M. R. Vanner , M. Aspelmeyer , M. S. Kim , and C. Brukner , Nat. Phys. 8 , 393 ( 2012 ). NPAHAX 1745-2473 10.1038/nphys2262 [16] 16 A. Albrecht , A. Retzker , and M. B. Plenio , Phys. Rev. A 90 , 033834 ( 2014 ). PLRAAN 1050-2947 10.1103/PhysRevA.90.033834 [17] 17 G. Gorelik , Phys. Usp. 48 , 1039 ( 2005 ). PHUSEY 1063-7869 10.1070/PU2005v048n10ABEH005820 [18] 18 M. P. Bronstein , Phys. Z. Sowjetunion 9.2–3 , 140 ( 1936 ). PHZSAL 0369-9811 [19] 19 R. Feynman , in Chapel Hill Conference Proceedings, 1957 . [20] 20 M. Bahrami , A. Bassi , S. McMillen , M. Paternostro , and H. Ulbricht , arXiv:1507.05733 . [21] 21 D. N. Page and C. D. Geilker , Phys. Rev. Lett. 47 , 979 ( 1981 ). PRLTAO 0031-9007 10.1103/PhysRevLett.47.979 [22] 22 C. Anastopoulos and B.-L. Hu , Classical Quantum Gravity 32 , 165022 ( 2015 ). CQGRDG 0264-9381 10.1088/0264-9381/32/16/165022 [23] 23 M. Derakhshani , C. Anastopoulos , and B.-L. Hu , J. Phys. Conf. Ser. 701 , 012015 ( 2016 ). JPCSDZ 1742-6588 10.1088/1742-6596/701/1/012015 [24] 24 Maaneli Derakhshani , arXiv:1609.01711 . [25] 25 C. Marletto and V. Vedral , Nature (London) 547 , 156 ( 2017 ). NATUAS 0028-0836 10.1038/547156a [26] 26 H. Pino , J. Prat-Camps , K. Sinha , B. P. Venkatesh , and O. Romero-Isart , arXiv:1603.01553v2 . [27] 27 C. Wan , M. Scala , G. W. Morley , ATM. A. Rahman , H. Ulbricht , J. Bateman , P. F. Barker , S. Bose , and M. S. Kim , Phys. Rev. Lett. 117 , 143003 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.117.143003 [28] 28 Shimon Machluf , Yonathan Japha , and Ron Folman , Nat. Commun. 4 , 2424 ( 2013 ). NCAOBW 2041-1723 10.1038/ncomms3424 [29] 29 C. Pfister , J. Kaniewski , M. Tomamichel , A. Mantri , R. Schmucker , N. McMahon , G. Milburn , and S. Wehner , Nat. Commun. 7 , 13022 ( 2016 ). NCAOBW 2041-1723 10.1038/ncomms13022 [30] 30 T. Krisnanda , M. Zuppardo , M. Paternostro , and T. Paterek , Phys. Rev. Lett. 119 , 120402 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.119.120402 [31] 31 See Supplemental Material http://link.aps.org/supplemental/10.1103/PhysRevLett.119.240401 for off-diagonal terms of the quantized gravitational field states and overcoming the experimental challenges, which contains Refs. [32–37]. [32] 32 M. Tomita and M. Murakami , Nature (London) 421 , 517 ( 2003 ). NATUAS 0028-0836 10.1038/nature01350 [33] 33 M. A. Weilert , D. L. Whitaker , H. J. Maris , and G. M. Seidel , Phys. Rev. Lett. 77 , 4840 ( 1996 ). PRLTAO 0031-9007 10.1103/PhysRevLett.77.4840 [34] 34 S. N. Gupta , Proc. R. Soc. A 65 , 161 ( 1952 ). [35] 35 Thai M. Hoang , Yue Ma , Jonghoon Ahn , Jaehoon Bang , F. Robicheaux , Zhang-Qi Yin , and Tongcang Li , Phys. Rev. Lett. 117 , 123604 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.117.123604 [36] 36 R. Casadio , A. Giugno , O. Micu , and A. Orlandi , Phys. Rev. D 90 , 084040 ( 2014 ). PRVDAQ 1550-7998 10.1103/PhysRevD.90.084040 [37] 37 S. Bose , K. Jacobs , and P. L. Knight , Phys. Rev. A 59 , 3204 ( 1999 ). PLRAAN 1050-2947 10.1103/PhysRevA.59.3204 [38] 38 R. Horodecki , P. Horodecki , M. Horodecki , and K. Horodecki , Rev. Mod. Phys. 81 , 865 ( 2009 ). RMPHAT 0034-6861 10.1103/RevModPhys.81.865 [39] 39 S. Roy Moulick and P. K. Panigrahi , Sci. Rep. 6 , 37958 ( 2016 ). SRCEC3 2045-2322 10.1038/srep37958 [40] 40 S. Dreser , R. Jackiw , and G. t. Hooft , Phys. Rev. Lett. 68 , 267 ( 1992 ). PRLTAO 0031-9007 10.1103/PhysRevLett.68.267 [41] 41a M. J. W. Hall and M. Reginatto , arXiv:1707.07974 ; 41b M. J. W. Hall and M. Reginatto , Phys. Rev. A 72 , 062109 ( 2005 ). PLRAAN 1050-2947 10.1103/PhysRevA.72.062109 [42] 42 H. B. G. Casimir and P. Polder , Phys. Rev. 73 , 360 ( 1948 ). PHRVAO 0031-899X 10.1103/PhysRev.73.360 [43] 43 J. Bateman , S. Nimmrichter , K. Hornberger , and H. Ulbricht , Nat. Commun. 5 , 4788 ( 2014 ). NCAOBW 2041-1723 10.1038/ncomms5788 [44] 44 J.-F. Hsu , P. Ji , C. W. Lewandowski , and B. D’Urso , Sci. Rep. 6 , 30125 ( 2016 ). SRCEC3 2045-2322 10.1038/srep30125 [45] 45 M. Frimmer , K. Luszcz , S. Ferreiro , V. Jain , E. Hebestreit , and L. Novotny , Phys. Rev. A 95 , 061801 ( 2017 ). PLRAAN 2469-9926 10.1103/PhysRevA.95.061801 [46] 46 N. Bar-Gill , L. M. Pham , A. Jarmola , D. Budker , and R. L. Walsworth , Nat. Commun. 4 , 1743 ( 2013 ). NCAOBW 2041-1723 10.1038/ncomms2771 [47] 47 H. S. Knowles , D. M. Kara , and M. Atatüre , Nat. Mater. 13 , 21 ( 2014 ). NMAACR 1476-1122 10.1038/nmat3805 [48] 48 K. Hornberger , J. E. Sipe , and M. Arndt , Phys. Rev. A 70 , 053608 ( 2004 ). PLRAAN 1050-2947 10.1103/PhysRevA.70.053608 [49] 49 O. Romero-Isart , Phys. Rev. A 84 , 052121 ( 2011 ). PLRAAN 1050-2947 10.1103/PhysRevA.84.052121 [50] 50 M. Carlesso and A. Bassi , Phys. Lett. A 380 , 2354 ( 2016 ). PYLAAG 0375-9601 10.1016/j.physleta.2016.05.034 [51] 51 C. Marletto and V. Vedral , arxiv:1707.06036v1 . [52] 52 J. Schmöle , M. Dragosits , H. Hepach , and M. Aspelmeyer , Classical Quantum Gravity 33 , 125031 ( 2016 ). CQGRDG 0264-9381 10.1088/0264-9381/33/12/125031 [53] 53 A. Mari , G. De Palma , and V. Giovannetti , Sci. Rep. 6 , 22777 ( 2016 ). SRCEC3 2045-2322 10.1038/srep22777 [54] 54 J. F. Donoghue , Phys. Rev. D 50 , 3874 ( 1994 ). PRVDAQ 0556-2821 10.1103/PhysRevD.50.3874 [55] 55 N. E. J. Bjerrum-Bohr , J. F. Donoghue , and B. R. Holstein , Phys. Rev. D 67 , 084033 ( 2003 ). PRVDAQ 0556-2821 10.1103/PhysRevD.67.084033 [56] 56 M. P. Blencowe , Phys. Rev. Lett. 111 , 021302 ( 2013 ). PRLTAO 0031-9007 10.1103/PhysRevLett.111.021302 [57] 57 T. Oniga and C. H.-T. Wang , Phys. Rev. D 93 , 044027 ( 2016 ). PRVDAQ 2470-0010 10.1103/PhysRevD.93.044027 [58] 58 C. Anastopoulos and B.-L. Hu , Classical Quantum Gravity 30 , 165007 ( 2013 ). CQGRDG 0264-9381 10.1088/0264-9381/30/16/165007

PY - 2017/12/13

Y1 - 2017/12/13

N2 - Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.

AB - Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.

UR - http://www.scopus.com/inward/record.url?scp=85038351399&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038351399&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.119.240401

DO - 10.1103/PhysRevLett.119.240401

M3 - Article

C2 - 29286711

AN - SCOPUS:85038351399

VL - 119

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 24

M1 - 240401

ER -