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### Mysteries of the Nano-World

Ephraim Fischbach

Physics Department

Purdue University

October 22, 2004

Ephraim Fischbach

Physics Department

Purdue University

October 22, 2004

Special Thanks to Dennis Krause (Wabash/Purdue), Ricardo Decca (IUPUI), and Daniel Lopez (Lucent)

Outline

- Quantum Cryptography
- Some basic ideas about encryption
- Essentials of nano-scale quantum mechanics
- Encryption via quantum mechanics
- A real device!
- The Force of Nothing:The Casimir Force
- The vacuum is never really empty
- Detecting vacuum fluctuations
- Nano-scale devices

Encryption and Everyday Life

- Codes used to be reserved for the military and diplomats.
- However, in today’s world, encryption affects all of us (e.g., credit card transactions over the Internet).
- Robust methods of encryption (such as the RSA method) will play an increasingly important role in our lives.

One-Time Keypad:An Unbreakable Code

Suppose Bob wishes to send a message to Alice:

Plain text message: HELLO ALICE

ASCII Binary Representation of Message:

Problem: Any protocol that assigns a different ASCII string to each “L” by some formula can eventually broken, especially if quantum computers come into being.

Encrypting the Message

Solution: Multiply the ASCII Binary Representation by a random string of 1’s and 0’s, which Alice and Bob each have, using the following rules:

1 1 = 0, 0 0 = 0, 1 0 = 1, 0 1 = 1

Same “L” encrypted differently

Key point: The encrypted message looks like a completely random string of 1’s and 0’s.

Decoding the Encrypted Message

Since Alice has the same one-time keypad (the string of random numbers used to multiply the binary message), she can easily decode the message:

Vulnerability of a One-time Keypad

Problem: Although a classical one-time keypad leads to an unbreakable code, the keypad itself may be compromised.

(A third party, Eve, may obtain a copy of the keypad and then eavesdrop and decode Alice and Bob’s communications without them knowing.)

Bob

Alice

Eve

Here is where quantum mechanics comes to the rescue !

Mini Review #1

- Any encryption technique which replaces the plain text with some other text according to a formula is subject to being cracked by a powerful enough computer.
- This is particularly true if quantum computers come into being.
- An unbreakable code can be constructed using a string of random 1’s and 0’s.
- However,such a “one-time keypad” is subject to being intercepted and copied.

The Rules of the Universe

Ordinary everyday objects obey the rules of classical mechanics (e.g., Newton’s laws of motion: F = ma, etc.)

But at very small distances (~size of an atom), the rules of classical mechanics no longer work.

~0.1 nanometer = one 10 billionth of a meter

A new set of rules is needed: Quantum Mechanics (QM)!!!

The Wacky World of Quantum Mechanics

Consider electrons which spin on their axes (as does the Earth) and so produce a magnetic field (as does the Earth), with North (N) and South (S) poles, just like a bar magnet:

N

S

For an ordinary bar magnet, one can find the direction the N pole points by simply looking at it. Furthermore, our looking does not affect where it points afterwards.

But in quantum mechanics, things are very different–the very act of observing the electron affects its state afterwards (Heisenberg Uncertainty Principle). This difference is tapped in quantum cryptography.

Direction of a Classical Magnet

Suppose you are given a bar magnet whose magnetic orientation is unknown. Ask the following questions:

Question #1: Is the vertical orientation or ?

Answer:

Question #2: Is the horizontal orientation or ?

Answer:

Question #3: Is the vertical orientation or ?

Answer:

Asking Question #2 does not affect the answer to Question #3 which follows it. The vertical orientation is unchanged.

Direction of a Quantum Magnet (Electron)

Now suppose you are given an electron whose magnetic orientation is unknown. Ask the same questions:

Question #1: Is the vertical orientation or ?

Answer:

Question #2: Is the horizontal orientation or ?

Answer:

Question #3: Is the vertical orientation or ?

Answer: (50%), (50%)

Asking Question #2 has affected the answer to Question #3!!

Application to Quantum Cryptography

Alice and Bob have a device located between them which randomly sends out entangled pairs of electrons in opposite directions with oppositely directed magnetic arrows:

In addition, Alice and Bob have orientation detectors which they then can use to measure the magnetic orientation of their electrons.

Now Alice and Bob independently decide which orientation (vertical or horizontal) they will measure.

Measurements of Orientation

Sample results for 6 trials:

If they measure the same orientation, their results are perfectly anti-correlated.

Eliminating Non-correlated Results

Alice and Bob then communicate by phone (not necessarily secure!) the orientations they measured for each electron pair. Using this information, they eliminate the trials in which they measured different orientations:

Converting Results to Numbers

Alice and Bob now have matched sets of arrows which they can convert to binary 1’s and 0’s using the following rules:

( or ) = 1 and ( or ) = 0

Alice gets 1001 while Bob gets 0110. Bob then interchanges 01 so they both get 1001.

Alice and Bob now have the same string of random numbers (1001) which can serve as the key for the one-time pad.

But is it secure?

Suppose Eve intercepts the electron going to Bob, measures its orientation, and then sends it to Bob in an attempt to obtain the one-time pad key:

Eve’s Eavesdropping Can Be Detected!

Since Eve doesn’t know which orientation Bob measures, she measures the Horizontal (H) or Vertical (V) orientations randomly, hoping she’ll guess correctly:

However, when Eve guesses incorrectly, her measurement will affect Bob’s measurement 50% of the time.

Alice and Bob notice something is amiss: For Pair #4, they both find their electrons have a orientation, which is impossible unless someone has intercepted and measured one of their electrons!

Mini Review #2

- The objective of quantum cryptography is to create the desired random strings of 1’s and 0’s in such a way that Alice and Bob would KNOW if there had been an eavesdropper.
- This can be achieved using a quantum device by taking advantage of the fact that in the quantum world observing a system disturbs it in a random way.
- Since an eavesdropper (Eve) would know with certainty that she would be detected this would remove any incentive she has for spying in the first place.

Quantum Cryptography has Gone Commercial!

www.magiqtech.com

The Force of Nothing:The Casimir Force

- In our everyday world, all forces arise from gravity and electromagnetism.
- At the nanoscale, new short-ranged forces become dominant.
- One of these new forces, the Casimir force, arises from quantum vacuum fluctuations.
- The Casimir force will affect the operation of any nano-scale mechanical device.

The Quantum Vacuum

A metal box at room temperature contains particles (air, dust,…) and radiation (light):

Removing particles and radiation leaves quantum vacuum fluctuations.

Lightning Protection

The metal body of a car protects you in case of a lightning strike because electric fields cannot penetrate through conductors.

The same mechanism explains how conducting plates change the electromagnetic field fluctuations of the vacuum.

Light Interacting with Glass Plates

Light passes through glass plates.

(Note: Slight shortening of wavelength inside the glass is not shown.)

Light Interacting with Metal Plates

Only certain colors are allowed between the plates

All colors of light are allowed outside the plates

Metal Plates Create a Light Pressure Difference

Pressure outside the plates is greater than the pressure between the plates so the plates are pushed together, i.e., feel an attractive force.

Poutside> Pinside

Poutside

Pinside

Poutside

Casimir Force

When the plates are less than 1 micron (0.001 mm) apartat room temperature, the light pressure difference due to virtual photons (quantum vacuum fluctuations) is greater than the pressure difference due to real photons. The resulting attractive force from virtual photons drawing the plates together is the Casimir force.

Classical Analog of the Casimir Force

A Casimir effect at Sea: Under certain conditions, ships lying close to one another are drawn together.

E. Buks and M. L. Roukes, Nature, 419, 119 (2002)

Casimir Force Between Two Pennies

1 Newton ~ 1/4 Pound

Gravitational Force:

~ weight of a E. Coli bacterium

~ 10-11 N

At 1 nm, the Casimir force between pennies > 700 pounds!

1 nanometer

IUPUI Casimir Force Experiment (Decca)

Sphere/Plate Separation: 200-1200 nm

Minimum Force (Static): : ~0.3 pN

(1 pN = 10-12 N)

(Note: E. Coli bacterium

weight ~ 10 pN)

Min. Pressure (Dynamic): ~0.6 mPa

Plate: 500 m 500 m 3.5 m

Sphere Radius: 300 m

Coatings:

Sphere: 1 nm Cr with 200 nm Au

Optical Fiber

“Self-Assembling”

Shutter

Fiber Core

Gold

Mirror

Hinges

Fiber Alignment Rails

Tilt-Mirror Variable Attenuator

- low voltage
- low insertion loss
- low PDL
- fast
- inexpensive

one and two fiber coaxial packages

Micromechanical Optical Crossconnect

I/O Fibers

256-mirror array

Imaging Lenses

Reflector

MEMS 2-axis Tilt Mirrors

Beam scanning during connection setup.

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