Although quantum gravity is a highly pursued research topic, the more basic question of whether

gravity is quantum has not yet been answered. Here we present a table-top experiment, feasible

with forseeable advances in technology, which can demonstrate that the Newtonian field from an

object is a bonafide quantum entity. This is demonstrated through the development of a verifiable

entanglement between two matter wave interferometers with mesoscopic objects as entanglement

between systems which are not directly interacting, can only be mediated by a quantum system

Barker, Peter

Bose, Sougato

Geraci, Andrew A.

Kim, M.S.

Mazumdar, Anuam

Milburn, Gerard

Morley, Gavin W.

Paternostro, Mauro

Toroš, Marko

Ulbricht, Hendrik

Enlighten

PoS(EDSU2018)045Testing the Quantum Coherent Behaviour of GravitySougato Bose∗Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BTLondon, UKE-mail: s.bose@ucl.ac.ukAnupam MazumdarVan Swinderen Institute University of Groningen 9747 AG Groningen, The NetherlandsGavin W. MorleyDepartment of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UKHendrik UlbrichtDepartment of Physics and Astronomy, University of Southampton, SO17 1BJ, Southampton, UKMarko TorošDepartment of Physics and Astronomy, University of Southampton, SO17 1BJ, Southampton, UKMauro PaternostroCTAMOP, School of Mathematics and Physics, Queen’s University Belfast, BT7 1NN Belfast, UKAndrew A. GeraciDepartment of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USAPeter BarkerDepartment of Physics and Astronomy, University College London, Gower Street, WC1E 6BTLondon, UKM. S. KimQOLS, Blackett Laboratory, Imperial College, London SW7 2AZ, UKGerard MilburnCentre for Engineered Quantum Systems, School of Mathematics and Physics, The University ofQueensland, QLD 4072 Australia.Although quantum gravity is a highly pursued research topic, the more basic question of whethergravity is quantum has not yet been answered. Here we present a table-top experiment, feasiblewith forseeable advances in technology, which can demonstrate that the Newtonian field from anobject is a bonafide quantum entity. This is demonstrated through the development of a verifiableentanglement between two matter wave interferometers with mesoscopic objects as entanglementbetween systems which are not directly interacting, can only be mediated by a quantum system.2nd World Summit: Exploring the Dark Side of the Universe25-29 June, 2018 - EDSU2018University of Antilles, Pointe-à-Pitre, Guadeloupe, France∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/PoS(EDSU2018)045Quantum Coherent Gravity Sougato Bose1. IntroductionIn this contribution, we are going to discuss our recent proposal for testing the quantum natureof gravity in a table-top experiment [1]. While the quantization of gravity is intensively pursued,and an unambiguous methodology to quantize gravity exists in the low energy limit, the lack ofempirical evidence has lead to the question of whether gravity is a quantum entity. For example,it is well established that the Newtonian field, with its characteristic ∼ 1r dependence can be pro-duced through the exchange of virtual (offshell) gravitons [2] between two objects. However, fromexisting experiments, such as the Newtonian force between two objects, it is not possible to estab-lish whether the field is quantum or classical. Indeed even the necessity of quantum gravity canbe questioned as a purely classical gravitational field, with action modified, can alleviate many ofthe oft-cited necessities for quantum gravity [3]. There are also hitherto untested mechanisms tomake quantum matter consistent with classical gravity [4, 5, 6, 7, 8, 9], making it imperative to askwhether gravity is quantum.Here we show that we can exploit a principle from quantum information theory, namely thatentanglement cannot be created by local operations and classical communications (LOCC) [10] toshow that gravity is indeed is a quantum entity. We essentially propose a feasible way of creatingquantum entanglement between two masses through their gravitational interaction. Witnessingsuch gravitationally mediated entanglement tests the quantum nature of gravity only if we maketwo crucial (but perfectly consistent with our current understanding of the world) assumptions: (a)the gravitational interaction between two masses is “mediated" by a field (in other words, it is nota direct interaction-at-a-distance), (b) the validity of a central principle of quantum informationtheory: entanglement between two systems cannot be created by Local Operatons and ClassicalCommunication (LOCC) [10]. That a classical entity going between two quantum objects cannotentangle them has also been shown in Refs.[11, 12]. Under this principle, since gravity conveysentanglement between separated masses, it serves as a quantum communication channel, and anyquantum communication channel must involve quantum entities travelling between parties (in thiscase the parties are the masses and the agent going between them is gravity).We first consider a schematic version that clarifies how the states of two neutral test massesm1 and m2, each held in a superposition of two spatially separated states |L〉 and |R〉 as shownin Fig.1(a) for a time τ , get entangled. Imagine the centres of |L〉 and |R〉 to be separated by adistance ∆x, while each of the states |L〉 and |R〉 are localized wavepackets so that we can assume〈L|R〉 = 0. There is a separation d between the centres of the superpositions as shown in Fig.1(a)so that even for the closest approach of the masses (d−∆x), the short-range Casimir-Polder force isnegligible (This means that the allowed distance of closest approach is d−∆x≈ 200µm, which isthe distance at which the Casimir-Polder interaction ∼ 0.1 of the gravitational potential, where, totake an explicit material, we have assumed R∼ 1µm radius diamond microspheres with dielectricconstant ε ∼ 5.7 [1]). Under these circumstances, the time evolution of the joint state of the twomasses 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)(1.1)1PoS(EDSU2018)045Quantum Coherent Gravity Sougato BoseΔx1dm1 m1Δx2m2 m2↑ ↓h00tτSpin Correlation Functions  Certifying Entanglement 0 ↑ ↓(a)	(b)	L,↑1R,↓1L,↑2R,↓2Figure 1: (a) Two test masses held adjacently in superposition of spatially localized states |L〉 and |R〉. (b) AdjacentStern-Gerlach interferometers are prepared in states |L,↑〉 j + |R,↓〉 j ( j = 1,2). Evolution under mutual gravitationalinteraction 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 entities – if all interactions aside gravity are absent, thenthis must be the gravitational field (labelled h00 where hµν are weak perturbations on the flat space-time metric ηµν ).This entanglement between test masses evidencing quantized gravity can be verified by completing each interferometerand measuring spin correlations.→ |Ψ(t = τ)〉12 =eiφ√2{|L〉11√2(|L〉2 + ei∆φLR |R〉2)+ |R〉11√2(ei∆φRL |L〉2 + |R〉2)} (1.2)where ∆φRL = φRL−φ ,∆φLR = φLR−φ , andφRL ∼Gm1m2τh̄(d−∆x), φLR ∼Gm1m2τh̄(d +∆x), φ ∼ Gm1m2τh̄d.One can now think of each mass as an effective “orbital qubit" with spatial states |L〉 and |R〉, whichwe can call orbital states. As long as 1√2(|L〉2 + ei∆φLR |R〉2) and 1√2(ei∆φRL |L〉2 + |R〉2) are not thesame state (which is very generic, happens for any ∆φLR +∆φRL 6= 2nπ , with integral n), it is clearthat the state |Ψ(t = τ)〉12 cannot be factorized and is thereby an entangled state of the two orbitalqubits. Note that we can getφRL ∼Gm1m2τh̄(d−∆x)∼ O(1) (1.3)if the duration for which we can hold the superposition without decoherence is τ ∼ 2s. Such asignificant phase accumulation leads to a significant entanglement between the masses as the en-tanglement increases monotonically over ∆φLR +∆φRL evolving from 0 to π and reaches maxiamlvalue for π . In practice, it is very difficult to witness directly the entanglement between the di-chotomized spatial orbital degrees of freedom as generated above as, for that, one will need to2PoS(EDSU2018)045Quantum Coherent Gravity Sougato Bosemeasure the spatial degrees of freedom in more than one spatial bases (which involves construct-ing ideal two port beam-splitters for massive objects). We next show how we naturally solve thisproblem by resorting to a modified version of the Stern-Gerlach (SG) interferometry which hasrecently been achieved with neutral atoms [13], and proposed for freely propagating nano-crystalswith embedded spins [14].The SG interferometry [cf. Fig. 1(b)] includes the following three steps on a neutral mass withan embedded electronic spin, a very low internal crystal temperature (77 K) – to prevent Black-body photons from decohering the superposition, and falling in a vacuum under very low ambientpressure (10−15Pa) to prevent atomic collisions from decohering the superposition:Step 1: A spin dependent spatial splitting of the centre of mass (COM) state of a test mass m j in aninhomogeneous magnetic field depicted by the evolution:|C〉 j1√2(| ↑〉 j + | ↓〉 j)→1√2(|L,↑〉 j + |R,↓〉 j), (1.4)where |C〉 is the initial localized state of m j at the centre 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 thesame ones as shown in Fig.1). For a micro-object of mass m j ∼ 10−14 kg, freely falling in an uni-form magnetic field gradient in the horizontal direction of ∼ 106 T m−1 [14] for a time τacc ∼ 500ms (with a suitable spin flip at half the time, so that the mass comes to a stop at time τacc), theseparation ∆x∼ 250µm between states |L,↑〉 j and |R,↓〉 j can be achieved.Step 2: "Holding" the coherent superposition created above (Eq.(1.4) for a time τ (Consider themagnetic field of the SG effectively switched off for a duration τ). This is accomplished by swap-ping the spin state from electronic spins to nuclear spins so that effectively the magnetic field is notseen any more by the spin and it stops accelerating/deccelerating and falls freely.Step 3: The third and final step brings back the superposition through the unitary transformations|L,↑〉 j→ |C,↑〉 j, |R,↓〉 j→ |C,↓〉 j, (1.5)which is, essentially, a backwards running of step 1).For our scheme, two such SG interferometers with neutral test masses m1 and m2 operatein parallel while being separated by about d ∼ 450 µm so as not to have a significant Casimir-Polder interaction. Moreover, for simplicity, we assume temporarily consider the accumulation ofa non-gravitational phase solely during the step 2 of the SG interferometry (by this way we areonly underestimating the phase that results in entanglement, not overestimating it). Due to theNewtonian interaction of the masses, the joint state of the two test masses evolves exactly as inEq.(1.1)-Eq.(1.2) 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.(1.2) of spin-orbital qubits with the step3 of Eq.(1.5), then we obtain the state at the end of the SG interferometry to be|Ψ(t = tEnd)〉12 =1√2{| ↑〉11√2(| ↑〉2 + ei∆φLR | ↓〉2)+ | ↓〉11√2(ei∆φRL | ↑〉2 + | ↓〉2)}|C〉1|C〉2,where the unimportant overall phase factor outside the state has been omitted. The above is man-ifestly an entangled state of the spins of the two test masses. It can be verified by measuring the3PoS(EDSU2018)045Quantum Coherent Gravity Sougato Bosespin correlations in two complementary bases in order to estimate as entanglement witness such asW = |〈σ (1)x ⊗σ (2)z 〉+ 〈σ (1)y ⊗σ (2)y 〉|. If W is found to exceed unity then the state is proven to beentangled, and, thereby, the mediator, the gravitational field, a quantum entity.While gravity is one of the fundamental forces, its weakness has made it difficult to test theo-ries on its nature. In particular it is important to answer the question, "is gravity a quantum entity?"Here, based on the principle that classical mediators cannot entangle [10], we have discussed anidea to solve this problem: to observe the entanglement of two test masses to ascertain whetherthe gravitational field is a quantum entity. Moreover, the prominence of our effect stems from avery simple fact: a Planck’s constant in the denominator fighting with the Gravitational constant inthe numerator of a relevant phase factor. The prescriptions we have provided for overcoming thechallenges (more details in the supplementary materials of Ref.[1]) will set out a roadmap towardsquantum gravity experiments and could have other beneficial spin-offs on the way, such as themeasurement of the Newtonian potential for microspheres [15] or compact meter-scale detectorsfor low frequency gravitational waves [16].References[1] Sougato Bose, Anupam Mazumdar, Gavin W Morley, Hendrik Ulbricht, Marko Toroš, MauroPaternostro, Andrew A. Geraci, Peter F. Barker, M. S. Kim, Gerard Milburn, Physical Review Letters119, 240401 (2017).[2] Anthony Zee. Quantum field theory in a nutshell. Princeton university press, 2010.[3] T. Biswas, E. Gerwick, T. Koivisto, and A. Mazumdar, Phys. Rev. Lett. 108, 031101(2012).[4] R. Penrose, Gen. Rel. Grav. 28, 581 (1996)[5] L. Diosi, Phys. Rev. A. 40, 1165 (1989)[6] A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013).[7] D. Kafri, J. M. Taylor, and G. J. Milburn, New J. Phys. 16, 065020 (2014).[8] A. Tilloy and L. Diósi, Phys. Rev. D 93, 024026 (2016).[9] J. Oppenheim, arXiv:1811.03116.[10] R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).[11] T. Krisnanda, M. Zuppardo, M. Paternostro, T. Paterek, Physical Review Letters 119, 120402 (2017).[12] C. Marletto, V. Vedral, Physical Review Letters 119, 240402 (2017).[13] Shimon Machluf, Yonathan Japha and Ron Folman, Nature Comm. 4, 2424 (2013).[14] 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).[15] J. Schmöle, M. Dragosits, H. Hepach, and M. Aspelmeyer, Class. Quantum Grav. 33, 125031 (2016).[16] R. J. Marshman, A. Mazumdar, G. W. Morley, P. F. Barker, S. Hoekstra, S. Bose, arXiv:1807.10830.4

Testing the Quantum Coherent Behaviour of Gravity

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Testing the Quantum Coherent Behaviour of Gravity

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