Transcript Quantum Entanglement on the Macroscopic Scale

Quantum Entanglement on
the Macroscopic Scale
By Jesse Ashworth
Bibliography
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Université de Genève. "What if quantum physics worked on a macroscopic level?
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ScienceDaily. ScienceDaily, 25 July 2013.
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and macro domains." Nature Physics (2013).
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"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