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TESTING QUANTUM MECHANICS

TOWARDS THE LEVEL OF EVERYDAY LIFE:

RECENT PROGRESS AND

CURRENT PROSPECTS

Anthony J. Leggett

Department of Physics University of Illinois at Urbana-Champaign USA

M ESO/MACROSCOPIC TESTS OF QM: M OTIVATION

At microlevel: (a) | ↑ 〉 + | ↓ 〉 quantum superposition 3 ≠ (b) | ↑ 〉 OR | ↓ 〉 classical mixture ×

how do we know? Interference

At macrolevel: (a) + quantum superposition

OR (b) OR macrorealism

Δ: Decoherence DOES NOT reduce (a) to (b)!

Can we tell whether (a) or (b) is correct? Yes, if and only if they give different experimental predictions. But if decoherence → no interference, then predictions of (a) and (b) identical. ⇒ must look for QIMDS quantum interference of macroscopically distinct states What is “macroscopically distinct”? (a) “extensive difference” Λ (b) “disconnectivity” D

Initial aim of program: interpret raw data in terms of QM, test (a) vs (b).

~large number of particles behave differently in two branches

The Search for QIMDS

1.Molecular diffraction*

(a.) Beam does not have to be monochromated

(b.) “Which-way” effects?

Oven is at 900–1000 K

⇒ many vibrational modes excited

4 modes infrared active ⇒

absorb/emit several radiation quanta on passage

through apparatus!

Why doesn’t this destroy interference?

( ) 3 e xp ( )^2 / 2 ( ~ 18 ) f υ = A υ − υ −υ (^) o (^) υ m (^) υ o i υ m

~100 nm

C (^60) z

z

I(z) ↑

---

*Arndt et al., Nature 401 , 680 (1999); Nairz et al., Am. J. Phys. 71 , 319 (2003).

Note:

The Search for QIMDS (cont.)

2. Magnetic biomolecules*

`

Raw data: χ(ω) and noise spectrum

above ~200 mK, featureless

below ~300 mK, sharp peak at ~ 1 MHz (ωres)

2 2 2 2 ω res (^) ≅ ω o + M H

A n ω o ~ a − bN ←^ no. of spins, exptly. adjustable Nb: data is on physical ensemble, i.e., only total magnetization measured.

*S. Gider et al., Science 268 , 77 (1995).

Apoferritin sheath (magnetically inert)

↑ ↓ ↑ ↑ ↓ ↑ = ↓ ↑ ↓ ↑ ↑ ↓ ~

.... (~5000 Fe 3+^ spins, mostly AF but slight ferrimagnetic tendency) α| 〉 + β| 〉? (M~200μB )

AF : Δ ~ = ω (^) o exp − N K / J

(isotropic) exchange en.

no. of spins uniaxial anisotropy

Interpretation of idealized expt. of this type: (QM theory ⇒) (^) δ J (^) x 1 δ J (^) y 1 ≥| J (^) z 1 | ~ N

1/ 2 ⇒ | δ J (^) x 1 | > N  But,

1 2

(exp t ) 0 (#)

xtot ytot

xtot x x

J J

J

J J

δ δ

δ δ δ

⇒ exactly anticorrelated with

⇒state is either superposition or mixture of |n,–n> but mixture will not give (#) ⇒ state must be of form

n^ |^ , n ∑ c^ n^ − n^ >

with appreciable weight for n ≤ N1/2. ⇒ high disconnectivity

Note: (a) QM used essentially in argument

(b) D ~ N 1/2^ not ~N. (prob. generic to this kind of expt.)

value of value of J (^) x1 J (^) x

“Macroscopic variable” is trapped flux Φ [or circulating current I]

The Search for QIMDS (cont.)

4. Superconducting devices ( : not all devices which are of interest for quantum computing are of interest for QIMDS) Advantages: — classical dynamics of macrovariable v. well understood — intrinsic dissipation (can be made) v. low — well developed technology — (non-) scaling of S (action) with D.

bulk superconductor

Josephson junction

RF SQUID

London^ trapped flux penetration depth

Josephson circuits

(10 4 –10 10 )

SYSTEM

~10 19 (10^3 –10^15 )

More possibilities for QIMDS:

(a) BEC’s of ultracold alkali gases:

Bose-Einstein condensates

(Gross-Pitaevskii)

Ordinary GP state:

( ( )^ ( )^ )

N

Ψ N = a ψ L r + b ψ R r

“Schrödinger-cat” state (favored if interactions attractive):

( ( )^ ) ( ( ))

N L

N

Ψ N = a ψ r + b ψ R r

problems:

(a) extremely sensitive to well asymmetry ΔΕ (energy stabilizing arg (a/b) ~tN^ ~ exp – NB/=) so ΔΕ needs to be exp’ly small in N

(b) detection: tomography unviable for N»1, ⇒ need to do time-sequence experiments (as in SQUIDS), but period v. sensitive e.g. to exact value of N

single-particle tunnelling matrix element

Ψ (^) L ( ) r^ Ψ^ R ( ) r

WHAT HAVE WE SEEN SO FAR?

1. If we interpret raw data in QM terms, then can conclude we have a quantum superposition rather than a mixture of meso/macroscopically distinct states. However, “only 1 degree of freedom involved.”
2. Do data exclude general hypothesis of macrorealism? NO
3. Do data exclude specific macrorealistic theories? e.g. GRWP ← Ghirardi, Rimini, Weber, Pearle

NO (fullerene diffraction: N not large enough, SQUIDS: no displacement of COM between branches)

Would MEMS experiments (if in agreement with QM) exclude GRWP?

alas:

⇒ do not gain by going to larger Δx (and small Δx may not be enough to test GRWP)

, ( )^2 Γ (^) col l ∝ Δ x Γ (^) d ce ∝ Δ x

decoherence rate acc. to QM

collapse rate in GRWP theory

HOW CONFIDENT ARE WE ABOUT (STANDARD QM’l) DECOHERENCE RATE?

Theory:

(a) model environment by oscillator bath (may be

questionable)

(b) Eliminate environment by standard Feynman-Vernon

type calculation (seems foolproof)

Result (for SHO):

ARE WE SURE THIS IS RIGHT?

Tested (to an extent) in cavity QED: never tested (?) on

MEMS.

Fairly urgent priority!

2

0

dec ~^ B

k T x x

⎛ ⎞^ ⎛^ Δ ⎞ Γ Γ (^) ⎜ ⎟ ⎜ ⎟ ⎝ Ω ⎠ ⎝ ⎠

i

provided kBT»=Ω

zero-point rms displacement

energy relaxation rate (Ω/Q)