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Quantum Entanglement on the Macroscopic Scale By Jesse Ashworth Bibliography Tiche, Malte C., Chae-Yeun Park, Minsu Kang, Hyunseok Jeong, and Klaus Molmer. "Is macroscopic entanglement a typical trait of many-particle quantum states?“ (2015). McIntyre, David H. Quantum Mechanics. N.p.: Pearson Education, Inc., 2012. 97- 105. Print. Pedigo, Daryl. "Quantum Computing: States and Gates." University of Washington. Seattle. Pedigo, Daryl. “Quantum Entanglement and Teleportation." University of Washington. Seattle. Jonhston, Hamish. "Diamonds entangled at room temperature." physicsworld.com 2 Dec. 2011. Université de Genève. "What if quantum physics worked on a macroscopic level? Researchers have successfully entangled optic fibers populated by 500 photons.“ ScienceDaily. ScienceDaily, 25 July 2013. Bruno, N et. al. "Displacement of entanglement back and forth between the micro and macro domains." Nature Physics (2013). Schirber, Michael. "Synopsis: Entangled Mirrors Could “Reflect” Quantum Gravity." APS Physics (2015). "Schrödinger's cat." Wikipedia. N.p., n.d. Quantum Entanglement: An Overview • An entangled state is a two-object quantum state for which measurements are both random and correlated. • Entanglement demonstrated in the EPR (Einstein-Podolsky-Rosen) thought experiment: • Spin-0 particle decays into two spin-1/2 particles, A and B • Particles move in opposite directions in the system’s CM-frame by conservation of momentum • Spin measurement of both A and B are completely random; there’s a 50% chance of measuring spin-up and a 50% chance of measuring spin-down • However, say you measure particle A to be spin-up—then particle B must be spin-down by conservation of angular momentum • “Spooky action at a distance” – Einstein Quantum Entanglement: An Overview • Mathematically, an entangled state is a two-object state which cannot be expressed as a tensor product of two one-object states. • Example of a non-entangled state: • Example of an entangled state: • For the second state: If you measure the first qubit to be a 0, then you know the second qubit is a 1. If you measure the first qubit to be a 1, then you know the second is a 0. Entangling a Two-Qubit State • The Hadamard operator (gate), denoted H, converts a pure qubit into a superposition state: • The controlled not gate (CNOT) acts on a two-qubit state; it changes the 2nd qubit from 0 to 1 or vice-versa if the first qubit is a 1: • One can entangle a state by applying the Hadamard gate to the first qubit and the CNOT gate to the resulting two-qubit state: From Micro to Macro: Motivation • Essentially, if two quantum objects are entangled and we measure some property of one object, then we know the property of the other. • Could this idea be extended to macroscopic objects? • For instance, could we entangle two electrical wires such that measuring the current in one wire instantly gives us information about the current in the other wire? Some Theoretical Underpinnings • Key question: How likely is macroscopic entanglement to occur? • As seen in the examples, an entangled state can be written as a superposition state, in which the object in question is (loosely speaking) in two different states at once. • Interactions with the system and its environment lead to decoherence, the process of a pure (single-phase) quantum state, superposition or not, becoming a statistical mixed state. • Larger systems interact to a greater extent with the environment, leading to far more rapid decoherence of macroscopic superposition (and thus entangled) states. Some Theoretical Underpinnings • Classical analogy: Gas of N particles in a box • Distribution of all gas particles on the left side of the box (b) corresponds to a macroscopically entangled state; homogeneous distribution (a) corresponds to a decohered, mixed state. • If the system is initially in a microstate in which all particles are on the left half of the box, it will rapidly relax to a more homogeneous distribution • Similarly, a macroscopically entangled state will rapidly decohere to a mixed state Image Source: http://arxiv.org/pdf/1507.07679v1.pdf The Quintessential Example: Schrödinger’s Cat • A box contains a radioactive nucleus, a Geiger counter, a bottle of cyanide gas, a hammer suspended over the bottle, and a cat • There is a 50% chance that the nucleus will decay in one hour, triggering the Geiger counter, releasing the Image Source: https://en.wikipedia.org/wiki/Schr%C3%B6dinger's_cat hammer, shattering the bottle, and poisoning • Can this situation be modeled quantum and killing the cat mechanically, and if so, how? The Quintessential Example: Schrödinger’s Cat • After one hour, the nucleus can be represented quantum mechanically as follows: • If the nucleus decays, then the cat dies, and if the nucleus does not decay, then the cat lives; one would then think that the state of the cat could be described as follows: • By the rules of quantum mechanics, the cat is essentially both alive and dead before the box is opened, counter to our intuition The Quintessential Example: Schrödinger’s Cat • Since the state of the nucleus and the cat are coupled, we can describe the entire system quantum mechanically as an entangled state: • However, by our earlier discussion, such a macroscopic state will quickly decohere to a statistical mixed state, meaning the cat is either alive or dead before we open the box • This result has been verified experimentally via an atom either in the ground or excited state corresponding to the nucleus and a classical electromagnetic field in a cavity corresponding to the cat • These results also agree with the Copenhagen interpretation, which says that one describes systems quantum mechanically only if they are microscopic; otherwise the systems are described classically Entangling Macroscopic Diamonds • In 2011, physicists successfully entangled high-energy vibrational states, or phonons, of two 3mm diamonds placed about 15cm apart • Experiment conducted at room temperature • Laser fired at a beam-splitter; each half of the resulting beam hit one of the diamonds • The photons hitting the beam splitter are put into a superposition of a photon traveling toward one diamond and a photon traveling toward the other Image Source: http://www.livescience.com/17264quantum-entanglement-macroscopic-diamonds.html Entangling Macroscopic Diamonds • When a photon from the laser hits one of the diamonds, energy is transferred from the photon to a phonon • Since the photon was originally in a superposition state, the phonon is also in a superposition of being in one diamond vs. being in the other • Thus, the diamonds are entangled via the superposed phonon • To confirm this, a second laser beam is fired at the beam splitter • One of the resulting photons will absorb the energy from the phonon • If the phonon was in a superposition, then the emitted photon will be in a superposition of coming from one diamond vs. coming from the other • This is confirmed by recombining the light from both diamonds and sending it through another beamsplitter; a superposed photon will always go through a particular port Entangling Macroscopic Diamonds • Results have implications for the development of quantum computing • Qubits, while they can be easily entangled, are easily annihilated via environmental interactions • Phonons in diamonds are far more shielded, and thermal fluctuations in the diamond typically do not impact the phonons • Information can be potentially stored by creating a phonon in a diamond via a laser pulse and recovering the information via another laser pulse Other Applications • Physicists in 2013 successfully entangled two optic fibers consisting of 500 photons each • Entanglement first achieved at the level of a single photon per fiber • More photons were then added to produce a larger entangled system • System reduced to the microscopic scale to verify that the system was still entangled • An experiment was proposed this past summer to test theories of nonrelativistic quantum gravity by entangling two 100g mirrors via a Michelson interferometer Conclusions • As demonstrated by the theory and the Schrödinger cat thought experiment, it is extremely difficult to create a macroscopic entangled state • The Copenhagen interpretation asserts the existence of a boundary between when quantum and classical mechanics can be used • Thus far that boundary is still fuzzy • Recent experiments have demonstrated that it is possible to entangle macroscopic systems, which could have implications in terms of the development of quantum computing, amongst other applications