Multicolor Quantum Entanglement

Paulo A. Nussenzveig

Instituto de Física - USP

The Team

Prologue• Do physical systems always possess well-defined individual properties, independent of our observations? Are such properties determined locally? These two “innocent” questions (when combined) have a negative answer in Quantum Mechanics. Surprisingly, the negative answer given by the theory is corroborated in experiments! Quantum systems may become entangled.

• What is quantum entanglement?

Einstein, Podolsky & Rosen’s paper

Einstein, Podolsky & Rosen’s paper

Entanglement

Measurements on one particle provide information about the state of the other. “Since at the time of measurement the systems no longer interact, no real change can take place in the second system as a consequence of anything that may be done to the first system.”

Entanglement and hidden variables

From 1935 to 1964/66, discussion about entanglement and its implications was mainly philosophical. Physicists such as David Bohm tried to “complete” Quantum Mechanics by creating hidden-variable theories, searching for a realist description of nature. The predominant view, however, is best described by a quote from Oppenheimer: “If we cannot disprove Bohm, then we must agree to ignore him”. John Nash (“A beautiful mind”) was captured by the subject. His biographer, Sylvia Nasar, said “...it was this attempt that Nash would blame, decades later in a lecture to psychiatrists, for triggering his mental illness – calling his attempt to resolve the contradictions in quantum theory, on which he embarked in the summer of 1957, ‘possibly overreaching and psychologically destabilizing’”

12

3

(a) 11, 22, or 33: RR and GG with the same frequency; never RG or GR

(b) 12, 13, 21, 23, 31, 32: RR and GG with the same frequency, ¼ of the total; ¾ the time RG or GR (same frequency)

1 23 1 2

3

(a) Particles have “instructions”: RRR, RRG, RGR, RGG, GRR, GRG, GGR, GGG. In order to explain case (a), it suffices to suppose the emitted particles are always identical.

(b) Let’s analyze case (b) under that hypothesis. Suppose the particles have the instruction RRG. Of six possible arrangements, only in cases 12 and 21 lights of the same color will turn on. Since all arrangements are supposed to be random, the same is true for RGR, RGG, GRR, GRG, and GGR. For instructions RRR and GGG, lights will always have the same color. Thus, the probability of having lights of the same color in case (b) should be over one third, results give only one quarter!

Conclusion: the experiment is incompatble with a description in terms of a set instructions defined a priori.

Field of research called Quantum Information

• Solution for communications problems (cryptography)

• Quantum Computing: more efficient computing by exploiting quantum parallelism. Limited number of algorithms (Shor’s factoring algorithm, Grover’s search algorithm). Simulation of complex quantum systems (important for the design of new materials).

Optical Parametric Oscillator (OPO)

α1out(t)

α2out(t)

α0in(t)

Pump (usually treated as classical field) generates twin photons (signal and idler) inside a cavity.Strong intensity correlations in the output beams.

Correlation measured by the subtraction of detector photocurrents.

i2 ∝ |α2out|2

-

Spectrum Analyzer

i1∝|α1out|2

PBS

δI1 - δI2 = 0

ω1 + ω2 = ω0

δϕ1 + δϕ2 = δϕ0

Energy conservation

Intensity CorrelationExperiment: A. Heidmann et al., Phys. Rev. Lett. 59, 2555 (1987) Theory: M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988)

Phase Anti-Correlation

Tripartite entanglement!

ν0ν1ν2

NO phonon noise

With phonon noise

Why don’t we have quantum computers yet?

The problem of decoherenceUseful quantum computers must operate on many qubits, generating many-particle entangled states (record of controlled entangled particles in the lab: 14). Why is it difficult to generate and store such states? The interaction with the environment leads to decoherence : things happen as if the environment were measuring the quantum system of interest, leading to a loss of indistinguishability and, thus, of coherence.

Famous example: “Schrödinger’s Cat” paradox (1935). Why don’t we observe state superpositions in the macroscopic (classical) world?

σ=1.14

0.0 0.2 0.4 0.6 0.8 1.00.5

0.6

0.7

0.8

0.9

1.0

1.1

Sym

plec

tic E

igen

valu

es P

T

1 - Losses

0.0 0.2 0.4 0.6 0.8 1.00.5

0.6

0.7

0.8

0.9

1.0

1.1

Sym

plec

tic E

igen

valu

es P

T

1 - Losses

σ=1.17

0.0 0.2 0.4 0.6 0.8 1.00.7

0.8

0.9

1.0

Sym

plec

tic E

igen

valu

es P

T

1 - Losses

σ=1.40

The effect of partial losses

Losses

1.0 1.1 1.2 1.3 1.4 1.5 1.60.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2S

ympl

ectic

Eig

enva

lues

PT

Pump power rel. to threshold power (σ )

Can there be such an ESD for bipartite Gaussian states?

Can there be such an ESD for bipartite Gaussian states?

Dual channel losses Single channel losses

Can there be such an ESD for bipartite Gaussian states?

Can there be such an ESD for bipartite Gaussian states?

Summary and Outlook 1st direct generation of entanglement between more than two “CV” subsystems (challenge): “quantum genealogy”. Multicolor quantum networks: require efficient storage and processing in the nodes; high-quality colorful entanglers; long-distance and short-distance communications via reliable quantum channels. Practical implementations (on-chip) under consideration. A thorough understanding of entanglement, this strange quantum phenomenon, remains a great challenge, hopefully a rewarding one.

Philosophy

Philosophy

“Philosophy is written in this grand book, the Universe, which stands continually open to our gaze. But it cannot be read unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.”

Galileu Galilei

Philosophy

The efficient simulation of quantum systems by means of quantum computers is akin to speed reading certain chapters of the grand book. We are still getting acquainted with this new “reading method” and acquiring the necessary tools. Hopefully, with quantum light we will not be kept much longer “wandering in the dark labyrinth”.

Rb MOT – EIT and/or FWM

How is this done in practice? We can, for example, do it with spin-1/2 particles, in a singlet state

2

↑ ↓ − ↓ ↑

Detectors are Stern-Gerlach-type with three possible alignments: aligned, or at ± 120o. The probability to measure opposite spins is cos2(θ/2). Detectors are coded with inverted colors. Inequalities were derived by J. S. Bell, Physics 1, 195 (1964). Measurements were made by: S. J. Freedman and J. S. Clauser, Phys. Rev. Lett. 28, 938 (1972) and A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. 47, 1804 (1982).

Can there be such an ESD for bipartite Gaussian states?

F. A. S. Barbosa et al., submitted to Phys. Rev. A